A boat travels 62 miles in 4 hours. For how long did the boat travel?
*Include a number and a unit on your answer (use all lower case letters for your units)
Blank 1:
Answers
On solving the provided question we can say that - by unitary method so in 1 hrs it will travel 62/4 = 15.5 miles
What is unitary method ?
The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
A boat travels = 62 miles
in = 4 hours
so in 1 hrs it will travel 62/4 = 15.5 miles
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Related Questions
Jacob spent 5 hours skiing and snowboarding. He skied for 2 hours 10 minutes.
How long did he spend snowboarding?
Answers
Answer:
he spent 2hours 50minutes snowboarding
the time he spent skiing and snowboarding minus the time he skied
5hours minus 2hours 10minutes
The jones brother, Carl,Cameron, and Carlos, are painters. Together they can paint a standard sized room in 2 hours. If Carl is alone on the job he can paint the room in 5 hours. If Cameron is alone he can paint the room in 6 hours.a)what equation can be used to determine how long it would take Carlos to paint the room alone? b)How long would it take Carlos to paint the room alone?
Answers
The workdone by the three(3) is equal to the painting of 1 room in 2 hours.
Time taken by
Carl alone = 5 hours
Cameron alone = 6 hours
Let time taken by Carlos alone = x hours
In One(1) hour, the size of the that will be covered by each of them is:
\(\begin{gathered} \text{Carl alone = }\frac{1}{5}\text{ of the room} \\ \text{Cameron alone=}\frac{1}{6}\text{ of the room} \\ \text{Carlos alone= }\frac{1}{x}\text{ of the room} \end{gathered}\)a) Hence, the equation that can be used to determine how long it would take Carlos to paint the room alone is:
\(\frac{1}{5}\text{ + }\frac{1}{6}\text{ + }\frac{1}{x}=\frac{1}{2}\)b) We will solve for the value of x in the equation above
\(\begin{gathered} \frac{1}{5}\text{ + }\frac{1}{6}\text{ + }\frac{1}{x}=\text{ }\frac{1}{2} \\ \\ \frac{1}{x}=\frac{1}{2}\text{ - }\frac{1}{5}\text{ - }\frac{1}{6} \\ \\ \frac{1}{x}=\frac{15-6-5}{30} \\ \\ \frac{1}{x}=\frac{4}{30} \\ \\ x=\frac{30}{4} \\ x=\frac{15}{2} \\ x=7.5\text{ hours} \end{gathered}\)Hence, it will take Carlos 7.5 hours to paint the room alone
The same sequence may be defined in three ways: 1) f(x) = 3x + 4 for x = {1, 2, 3, ...}, 2) a1 = 4 and an + 1 = an + 3 for n = {1, 2, 3, ...} and 3) an = 4 + 3(n − 1) for n = {1, 2, 3, ...}.
They are all supposed to generate the same values, but one version may contain an error. If one version contains an error, identify the one with the error and fix it.
Answers
Answer:
its B
Step-by-step explanation:
al Thinking and Logic: Practice
Question 4 of 5
Select the correct answer from each drop-down menu.
Complete the contrapositive of the following statement.
If x is a multiple of 10, it is an even number.
If x is
then it is
Submit
Answers
The contrapositive of the statement "If x is a multiple of \(10\), it is an even number" is "If \(x\) is not a multiple of \(10\), then it is not an even number."
To complete the contrapositive of the statement "If \(x\) is a multiple of \(10\), it is an even number," we need to negate and reverse the original statement.
The original statement can be represented as:
\(\[P: \text{If } x \text{ is a multiple of 10, then } x \text{ is an even number.}\]\)
The negation of this statement is:
\(\[\neg P: \text{If } x \text{ is not an even number, then } x \text{ is not a multiple of 10.}\]\)
To form the contrapositive, we reverse the implications:
\(\[\text{Contrapositive: If } x \text{ is not a multiple of 10, then } x \text{ is not an even number.}\]\)
In symbolic notation, the contrapositive would be:
\(\[\text{Contrapositive: } \neg P: \text{If } \neg(x \text{ is a multiple of 10}), \text{ then } \neg(x \text{ is an even number}).\]\)
Therefore, the contrapositive of the statement "If x is a multiple of \(10\), it is an even number" is "If \(x\) is not a multiple of \(10\), then it is not an even number."
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Please, help it is geometry
Answers
Answer:
WR ≈ 13.862
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
WR² + RT² = WT²
WR² + 12.1² = 18.4²
WR² + 146.41 = 338.56 ( subtract 146.41 from both sides )
WR² = 192.15 ( take the square root of both sides )
WR = \(\sqrt{192.15}\) ≈ 13.862 ( to the nearest thousandth )
Please help thank you all so much
Answers
The domain of the composite functions:
a). (f + g)(-2) = 23
b). (f - g) (-2) = 1
c). f(x) - g(x) = x² - 5x - 13
What is composite function?A function is composite when the co- domain of the first mapping is the domain of the second mapping
Given the functions f(x) = x² - 4x and g(x) = x + 13, we shall evaluate the domains of the functions as follows:
a). (f + g)(-2) = (-2)² - 4(-2) + (-2) + 13
(f + g)(-2) = 4 + 8 - 2 + 13
(f + g)(-2) = 23
b). (f - g) (-2) = (-2)² - 4(-2) - (-2) - 13
(f - g)(-2) = 4 + 8 + 2 - 13
(f - g) (-2) = 1
c). f(x) - g(x) = x² - 4x - x - 13
f(x) - g(x) = x² - 5x - 13
Therefore, the domain of the composite functions:
a). (f + g)(-2) = 23
b). (f - g) (-2) = 1
c). f(x) - g(x) = x² - 5x - 13
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simplify theta(sin theta) ²/2tan theta
Answers
Step-by-step explanation:
When θ is very small, θ ≈ sin θ ≈ tan θ.
θ (sin θ)² / (2 tan θ)
θ³ / (2θ)
θ² / 2
5. There are 400 students in the senior class at Oak Creek High School. All 2 points
of these students took the SAT. The distribution of their SAT scores is
approximately normal. The number of students who scored within 2
standard deviations of the mean is approximately *
-3
-2
0
1
2.
3
Answers
Answer:
The number of students who scored within 2 standard deviations of the mean is 380.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
The number of students who scored within 2 standard deviations of the mean is approximately
By the Empirical Rule, 95% of the students scored within 2 standard deviations of the mean
Out of 400
0.95*400 = 380
The number of students who scored within 2 standard deviations of the mean is 380.
Answer: 380
Step-by-step explanation: 95% of 400 is 380
2 + 2. what is the sum
Answers
Answer: 4
Step-by-step explanation:
Answer:4
2+2=4 if I have two apples and pick up two more I now have 4 total
Calculate the distance between the points P=(1, -1) and N=(5, -8) in the coordinate plane.
Round your answer to the nearest hundredth.
PLEASE PLEASE HELP ME
Answers
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06\)
Hello i need some help!
Answers
Answer:
3×2 + 3×-b
Step-by-step explanation:
\(3(2-b)\\= 3\times 2 + 3\times (-b)\\\\= 6 -3b\)
In the distributive property you are distributing the number outside the parentheses to the numbers inside.
15 POINTS
Using Pythagoras' theorem, calculate the length
of XY.
Give your answer in centimetres (cm) to 1 d.p.
Answers
Answer:
13.27 cm
Step-by-step explanation:
I am using (xy) to mean the length of the side xy
7^2 + (xy)^2 = 15^2
49 + (xy)^2 = 225
(xy)^2 = 225-49
(xy)^2 = 176
Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm
13.3cm
Step-by-step explanation:
The Pythagorean theorem is a^2+ b^2 = c^2
Plug the values into the equation.
7^2+ b^2 = 15^2
Simplify.
49 ÷ b^2 = 225
Subtract 49 from both sides.
b^2 = 176
Take the square root of both sides.
vb^2 = v176
b=13.266
b=13.3cm
Solve 4cos(4x)=2
for the smallest three positive solutions.
Give your answers accurate to at least two decimal places, as a list separated by commas.
Answers
4cos(4x) = 2
Dividing both sides by 4:
cos(4x) = 1/2
Using the inverse cosine function, we find the angles where cos(4x) = 1/2:
4x = ±π/3 + 2πn, where n is an integer
x = ±π/12 + (π/2)n, where n is an integer
To find the smallest three positive solutions, we need to start with n = 0 and find the first three positive solutions:
x = π/12, 7π/12, and 13π/12
Rounding to two decimal places, the smallest three positive solutions are:
x = 0.26, 0.61, and 1.08
Therefore, the solutions are 0.26, 0.61, and 1.08, separated by commas.
Can someone help please?
ASAP
Answers
Answer:
Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)
Step-by-step explanation:
As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.
11^2 + 5^2 = AC^2
121 + 25 = AC^2
146 = AC^2
sqrt(146) = AC^2
Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)
diana is 50 years old and has recently started experiencing a few symptoms of menopause. which of the following symptoms is diana most likely to experience?
Answers
Diana is most likely to experience hot flashes, night sweats, and irregular periods as symptoms of menopause.
Menopause is the time in a woman's life when her period stops, usually occurring naturally after age 45. A gap of 12 months without a menstrual period diagnoses menopause. Common symptoms include hot flashes, night sweats, and irregular periods.
Diana is most likely to experience hot flashes, night sweats, and vaginal dryness. These are the most common symptoms of menopause and can start before a woman reaches her 50s. Other symptoms may include mood swings, difficulty sleeping, and changes in libido.
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Frame a linear equation for each of the following statements.
1. \(b\)47 is 23 more than two times p.
2.\(b\)One-fourth of p decreased by 3 gives −12
3.\(b\)2 times p exceeds 15 by 3.
4. \(b\)One-fifth of p decreased by 4 gives 6
Answers
Answer: chopstick
Step-by-step explanatio
Each side length of a triangle is 4 cm. What type of triangle is it?
☐ right
□acute
Equilateral
Isosceles
Answers
Answer: Equilateral
Step-by-step explanation:
It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.
Hope you understood.
What are the coordinates of the graphed point? An x y coordinate system. The x axis extends from negative 5 to 5, and y axis extends from negative 5 to 5, with whole numbers marked on the grid. A point is marked 3 units to the left of the y axis and 2.5 units up from the x axis. CLEAR CHECK (2.5, −3) 2.5 , (−3, −2.5) -3 , (3, −2.5) 3 , (−3, 2.5)
Answers
The Coordinates of the graphed point are (−3, 2.5).
The coordinates of the graphed point, based on the given description, are (−3, 2.5).
The x-coordinate represents the horizontal position of the point, and it is described as being 3 units to the left of the y-axis. Since the y-axis is the vertical line passing through x = 0, moving 3 units to the left means the x-coordinate is −3.
The y-coordinate represents the vertical position of the point, and it is described as being 2.5 units up from the x-axis. Since the x-axis is the horizontal line passing through y = 0, moving 2.5 units up means the y-coordinate is 2.5.
Therefore, the coordinates of the graphed point are (−3, 2.5).
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HELP PLEASE!!
Quadrilateral CDEF is a rhombus. What is m
Answers
Answer:
∠ BDC = 29°
Step-by-step explanation:
the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then
∠ BCD = ∠ BED = 61°
• the diagonals are perpendicular bisectors of each other , then
∠ CBD = 90°
the sum of the 3 angles in Δ BCD = 180°
∠ BDC + ∠ CBD + ∠ BCD = 180°
∠ BDC + 90° + 61° = 180°
∠ BDC + 151° = 180° ( subtract 151° from both sides )
∠ BDC = 29°
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in
x = 18.19 kgf/cm2 for the modified mortar (m = 42) and y = 16.87 kgf/cm2 for the unmodified mortar (n = 32). Let m1 and m2 be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.
(a) Assuming that ?1 = 1.6 and ?2 = 1.3, testH0: m1 ? m2 = 0 versus Ha: m1 ? m2 > 0 at level 0.01.
State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to two decimal places.)
z ? z ? Compute the test statistic value. (Round your answer to two decimal places.)
z = State the conclusion in the problem context.
Reject H0. The data does not suggest that the difference in average tension bond strengths exceeds 0.
Fail to reject H0. The data does not suggest that the difference in average tension bond strengths exceeds from 0.
Fail to reject H0. The data suggests that the difference in average tension bond strengths exceeds 0.
Reject H0. The data suggests that the difference in average tension bond strengths exceeds 0.
Answers
the data suggests that the difference in average tension bond strengths is greater than 0. In other words, the polymer latex modified mortar has a higher tension bond strength than the unmodified mortar.
a) The rejection region for this one-tailed hypothesis test is z ? z > 2.33.
The test statistic value is z = 2.76.
Therefore, the conclusion is that we reject H0. The data suggests that the difference in average tension bond strengths is greater than 0.
For this one-tailed hypothesis test, we must reject the null hypothesis (H0: m1 - m2 = 0) if the test statistic is greater than 2.33. Our test statistic value is 2.76, which is greater than 2.33, so we reject H0. This indicates that the data suggests that the difference in average tension bond strengths is greater than 0. In other words, the polymer latex modified mortar has a higher tension bond strength than the unmodified mortar.
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A line goes through the point (−4, 1) and goes through the origin. Which of the following is the correct equation of the line?
y= -4x
y= 4x
y= -1/4x
y= -1/4x+1
y= x-4
Answers
Use the following sets to answer the question.
A={1,2,3,4,5}
B={5,6,7,8}
Which answer shows the union of sets A
and B?
{5}
{1,2,3,4,6,7,8,9}
{1,2,3,4,5,6,7,8}
{2,4,8}
Answers
The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.
The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.
To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.
Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.
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which of the following best describes the set of all numbers in the form a+bi, where a and b are real numbers and i equals √-1?
Answers
The Solution:
Given that a number is defined as below:
\(a+bi\)Required:
Find the best description for the number.
\(The\text{ number is a complex number.}\)The correct answer is [ option C]
Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Answers
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
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Which of the following is between 1/5 and 2/3?
0.15
5/7
0.3
1/6
None of these
Answers
Answer:
5/7 I got this one it was 5/7
Find the number that belongs
in the green box.
Round your answer to the nearest tenth.
Answers
Answer:
1.2 (to one tenth)
Step-by-step explanation:
Hope that helps :-)
Answer:
Step-by-step explanation:
Remark
You are going to have to find the angle on the lower right before you can get the answer. Call the angle on the lower right = x
Equation
Sin(60)/7 = sin(x) / 3
Solution
3 * sin(60) / 7 = sin(x)
Sin(60) = 0.866
3*0.866 / 7 = sin(x)
sin(x) = 0.3712
x = sin-1(0.3712)
x = 21.79
Now calculate the 3rd angle call it y
y + 21.79 + 60 = 180
y + 81.79 = 180
y = 180 - 81.79
y = 98.21
Now use the sin law again.
Let ? = z
z/sin(98.21) = 7/sin(60) Multiply both sides by sin(98.21)
z = 7 * sin(98.21) / sin(60)
z = 6.9282 / sin(60)
z = 8
? = 8
A tin of Tonyz soup has a paper label wrapped around the outside. The tin has a height of 21cm and a radius of 7cm. The label covers the entire height of the can. The label overlaps by 1cm as it wraps around so that it can be stuck together. Calculate the area of the label. 7cm Tonyz Cream of EST 1986 EST Tomato Soup VRISTES 14.1 OZ (40g) 12 21cm
Answers
Answer:
944.6 cm²
Step-by-step explanation:
You want the area of a label that covers the lateral surface of a cylinder with a 1 cm overlap of the ends. The cylinder is 7 cm in radius and 21 cm high.
CircumferenceThe circumference of the cylinder is ...
C = 2πr
C = 2π(7 cm) = 14π cm ≈ 43.982 cm
AreaThe area of the label is the product of its length and width. The length is 1 cm more than the circumference, so the area is ...
A = LW = (43.982 +1 cm)(21 cm) ≈ 944.6 cm²
The area of the label is about 944.6 cm².
Camille is comparing different apartment complexes. Here is the data she collected. Complex name Bedrooms Bathrooms Rent Rent includes heat Amenities Grand Vistas 2 br 2 bath $990 no fitness center, pool ; Maple Ridge 2br 1.5 bath , $685 yes fitness center, pool; Old Mill 2 1.5, 790 no pool; Willow Brook 2br 2bath $885 no jacuzzi. The individuals in this data set are:
Answers
The individuals in this data set are the different apartment complexes: Grand Vistas, Maple Ridge, Old Mill, and Willow Brook.
The individuals in this data set are the different apartment complexes that Camille is comparing. The data provides information on the complex name, number of bedrooms and bathrooms, rent amount, whether rent includes heat, and the amenities offered.
Grand Vistas:
Bedrooms: 2
Bathrooms: 2
Rent: $990
Rent includes heat: No
Amenities: Fitness center, pool
Maple Ridge:
Bedrooms: 2
Bathrooms: 1.5
Rent: $685
Rent includes heat: Yes
Amenities: Fitness center, pool
Old Mill:
Bedrooms: 2
Bathrooms: 1.5
Rent: $790
Rent includes heat: No
Amenities: Pool
Willow Brook:
Bedrooms: 2
Bathrooms: 2
Rent: $885
Rent includes heat: No
Amenities: Jacuzzi
Each apartment complex is represented as an individual in the data set. Camille has collected specific details for each complex, including the number of bedrooms and bathrooms, the rent amount, whether heat is included in the rent, and the amenities provided.
This data set allows Camille to compare different apartment complexes based on these attributes. She can evaluate factors such as rent prices, included amenities, and the presence of heat in the rent. This information will assist Camille in making an informed decision about which apartment complex may be the most suitable for her needs and preferences.
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Jake cuts out five-pointed stars. They are different sizes, but they
all have the same shape. The side lengths within
each star are the same.
To find the perimeter of each star, Jake uses the expression
12€ + 1 – 46 – 8.5 + 2€ + 8, where l is the side length of the star.
a. Find the perimeter of a star with side length 6 inches. Show your work.
Answers
Answer:
60
Step-by-step explanation: 12L + 1/2 = 72.5
72.5 - 24 - 8.5 + 20
72.5 -24 = 48.5 - 8.5 = 40
40 + 20 = 60
The perimeter of a star with side length 6 inches is,
⇒ 38.5 inches.
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
Jake uses the expression 12l + 1 – 46 – 8.5 + 2l + 8, where l is the side length of the star.
Hence, The perimeter of a star with side length 6 inches is,
⇒ 12l + 1 – 46 – 8.5 + 2l + 8
⇒ 12 × 6 + 1 - 46 - 8.5 + 2×6 + 8
⇒ 72 + 1 - 46 - 8.5 + 12 + 8
⇒ 38.5 inches.
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Find the equation for the line that passes through (-1, 10) that has slope 5/7. You do not need to simplify.
Give your answer in point-slope
Answers
Answer:
y = (5/7)x + (75/7)
Step-by-step explanation:
If you ever find yourself in a math class where you have to write the equation of a line that goes through a certain point and has a certain slope, don't panic. There is a simple formula that can help you out. It's called the point-slope form and it looks like this:
y - y1 = m (x - x1)
It may look scary, but it's actually pretty easy to use. All you have to do is plug in the values that you know and solve for the ones that you don't. For example, let's say you have a line that passes through the point (-1, 10) and has a slope of 5/7. You can use the point-slope form to write the equation of the line like this:
y - 10 = (5/7) (x - (-1))
See? That wasn't so bad. Now you can simplify the equation by distributing the 5/7 and adding 10 to both sides. You get:
y = (5/7)x + (75/7)
And that's it! You have written the equation of the line in slope-intercept form, which is another way of writing the equation of a line. You can check your answer by plugging in the values of x and y from the original point and seeing if they make the equation true. If they do, you're good to go. If not, you made a mistake somewhere and you should go back and fix it.
Congratulations! You have learned how to use the point-slope form to write the equation of a line. Now you can impress your math teacher and your friends with your skills. Remember, with great power comes great responsibility.
✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧