Use the Law of Sines to solve the triangle. Round your answers to two decimal places.A = 8° 40', B = 13° 15', b = 4.8
Answers
Given
[tex]A=8°40^{\prime},B=13°15^{\prime},b=4.8[/tex]To find the value of a, c, C.
Explanation:
It is given that,
[tex]A=8°40^{\prime},B=13°15^{\prime},b=4.8[/tex]Since,
[tex]A=8°40^{\prime},B=13°15^{\prime}[/tex]Then,
[tex]\begin{gathered} A+B+C=180 \\ 8\degree40^{\prime}+13\degree15^{\prime}+C=180\degree \\ C=180\degree-21\degree55^{\prime} \\ C=(179-21)\degree(60^-55^)^{\prime} \\ C=158\degree5^{\prime} \end{gathered}[/tex]Therefore, by using Sine law,
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin8\degree40^{\prime}}{a}=\frac{\sin13\degree15^{\prime}}{4.8}=\frac{\sin158\degree5^{\prime}}{c} \\ \Rightarrow\frac{\sin8\degree40^{\prime}}{a}=\frac{\sin13\degree15^{\prime}}{4.8} \\ \Rightarrow\frac{\sin13\degree15^{\prime}}{4.8}=\frac{\sin158\degree5^{\prime}}{c} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \begin{equation*} \frac{\sin8\degree40^{\prime}}{a}=\frac{\sin13\degree15^{\prime}}{4.8} \end{equation*} \\ \frac{0.14608}{a}=\frac{0.227501}{4.8} \\ a=\frac{0.14608}{0.047396} \\ a=3.08211 \\ a=3.1 \end{gathered}[/tex]Also,
[tex]\begin{gathered} \begin{equation*} \frac{\sin13\degree15^{\prime}}{4.8}=\frac{\sin158\degree5^{\prime}}{c} \end{equation*} \\ 0.047396=\frac{0.366501}{c} \\ c=\frac{0.366501}{0.047396} \\ c=7.73274 \\ c=7.7 \end{gathered}[/tex]Hence, the answer is
[tex]C=158\degree5^{\prime},a=3.1,c=7.7[/tex]Related Questions
In \triangle NOP,△NOP, \overline{PN}\cong \overline{OP} PN ≅ OP and \text{m}\angle P = 50^{\circ}.m∠P=50 ∘ . Find \text{m}\angle O.m∠O.
Answers
The value of the measure of ∠O will be 65°
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In ΔNOP;
PN ≅ OP
So, ∠O = ∠N
And, Measure of ∠P = 50°
Now,
In the ΔNOP;
The sum of all the three angles are 180°.
The value of the measure of ∠O = x
We get;
∠O + ∠N + ∠P = 180°
Substitute ∠P = 50° and ∠O = ∠N = x we get;
x + x + 50 = 180
2x + 50 = 180
2x = 180 - 50
2x = 130
x = 65
Thus, The value of the measure of ∠O will be 65°.
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Blake buys a one-quart bottle of juice for $6.40. What is the unit rate of the cost ofthe juice per fluid ounce?1 gallon 4 quarts1 quart 2 pints1 pint cups1 cup= 8 fluid ounces2Before you try that problem, answer the question below.How many fluid ounces of juice did Blake buy?
Answers
So the information we have is Blake buys a one-quart bottle of juice for $6.40
So we can say the juice cost 6.40 $/quart
so now, let's find the relationship between quart and ounces
1 quart =2 pints
1 pint =2 cups
1 cup = 8 fluid ounces
So
[tex]\begin{gathered} 1\text{quart}=2\text{ pints=2}\cdot(2\text{ cups)} \\ 1\text{ quart= 4 cups} \\ 1\text{ quart=4}\cdot(8\text{ ounces)} \\ 1\text{ quart=32 ounces} \end{gathered}[/tex]so for the question:
How many fluid ounces of juice did Blake buy?
she bought 1 quart of juice and we said 1 quart=32 ounce, so the answer is: She bought 32 ounces of juice.
And for the first question: What is the unit rate of the cost of
the juice per fluid ounce? we can do:
[tex]6.40\frac{Dollars}{quart}\cdot\frac{1\text{ quart}}{32\text{ ounces}}=\frac{6.40}{32}\frac{dollars}{ounces}[/tex]So the answer is:
0.2 $/ounces ($ per ounce)
Express x^2-3x+1 in the form (x-p)^2+q
Answers
By algebra properties, the equation x² - 3 · x + 1 in the form (x - p)² + q is equal to (x - 3 / 2)² - 5 / 4.
How to simplify a quadratic equation by completing the square
Completing the square is a method used to simplify quadratic equations of the form a · x² + b · x + c that are not perfect squares, where a part of it becomes into perfect square and is simplified. This can be found by using algebraic methods. The complete procedure is shown below:
x² - 3 · x + 1
(x² - 3 · x + 1) + 0
(x² - 3 · x + 1) + [9 / 4 + (- 9 / 4)]
(x² - 3 · x + 9 / 4) + [1 + (- 9 / 4)]
(x - 3 / 2)² - 5 / 4
The quadratic equation is equivalent to (x - 3 / 2)² - 5 / 4.
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how do you rewrite an expression with parenthesisthe question is 5(x+2)
Answers
We have the following:
[tex]5(x+2)=5x+10[/tex]the answer is 5x + 10
this is geometry please help
Answers
Answer: 1st one is sometimes
2nd one is always
3rd one I think is always
4th one is always
Step-by-step explanation:
1st one the sum must equal 90 so either one could be greater
2nd one vertical angles always equal each other
3rd one if B is the midpoint it would be AB BC
4th one it will always equal 180
The Epson Stylus 850 can print Helen's class project in 12 minutes. The Epson Stylus 500 can print the project in 42 minutes. If the two printers work together, how long would they take to print out the project?A) 9 minB) 9 1/3 minC) 84 minD) 3/28 min
Answers
The epson stylus 850 can print Helen's project in 12 mins
TThe epson stylus 500 can print that same project in 42 minutes
Work = rate x time
the two printers are working on the same assignment
therefore, we will be adding their rate
for epson 850
work = rate x time
work= 1
time = 12mins
1 = rate x 12
make rate the subject of the formula by dividing bott sides by 12
1 / 12 = rate x 12 / 12
rate = 1/ 12
for epson 500
work = rate x time
time = 42 mins
work = 1
applying the same process
1 = rate x 42
rate = 1/42
since they are both working together
Total rate = 1 /12 + 1/42
lcm is 84
since 12 and 42 are factors of 84
Total rate = 1/12 + 1/42
total rate = 84 * 1 /12 + 84*1 / 42 /84
total rate = 7 + 2 / 84
total rate = 9/84
to calculate the time they worked together
work = rate x time
1 = 9/84 x time
make time the subject of the formula
1 / 9/84 = time
time = 84/9
time = 28 / 3
Time = 9 1/3 min
Option B
Divide. Round your answer to the
nearest whole number.
3.37 54.308
Answers
Answer:
16
Step-by-step explanation:
Solve the following equation for all values of x:2 +3−28=9+27
Answers
McMichael Inc. collects 25% of its sales on account in the month of the sale and 75% in the month following the sale. If sales on account are budgeted to be $523,000 fo September and $465,000 for October, what are the budgeted cash receipts from sales on account for October?
Answers
The budgeted cash receipts from sales on account for October is $479500.
Define sale.A sale is a deal in which two or more parties exchange goods or services for cash or other assets. A sale in the financial markets is an arrangement involving the cost of a security and its delivery for agreed-upon payment between a buyer and a seller. Sales in general business operations refer to any exchanges of money or value for the right to possess a good or get a service. Sales, in the context of accounting, refers to the income generated by a corporation via the selling of goods or services (net sales).
Given Data
McMichael Inc. collects 25% of its sales on account in the month of the sale and 75% in the month.
If sales on account are budgeted to be $523,000 to September and $465,000 for October.
We can respond as follows based on the data provided in the question:-
25% of sales from October plus 75% of sales from September equal the budgeted cash receipts from sales.
Sales revenue budgeted for in cash is
($523,000 (25%)) + ($465,000 (75%))
130750 + 348750
479500
The budgeted cash receipts from sales on account for October is $479500.
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Kai took five tests this semester. His scores are listed below. 92, 88, 90, 96, 84What is the mean absolute deviation of Kai's test scores?4.03.22.01.6
Answers
the mean can be calculate with this equation:
[tex]m=\frac{x_1+x_2+\cdots}{n}[/tex]So in our problem will be:
[tex]\begin{gathered} m=\frac{92+88+90+96+84}{5} \\ m=90 \end{gathered}[/tex]A.) If angle 3 = 5x-1 and angle 5-3x+11, then x= B.) If angle 3 = 5x-1, and angle 5 = 3x + 11, then the measure of angle 3= C.) If 23 = 5x-1, and 25 = 3x+ 11, then the measure of angle 1= D.) If angle 3 = 5x-1, and angle 5 = 3x + 11, then the measure of angle 2 =
Answers
1) Gathering the data
∠3 = 5x -1
∠5=3x +11
∠3=?
2) The angles ∠3 and ∠5 are alternate interior angles, therefore they are congruent ones. So we can write:
5x -1 = 3x +11
5x -3x = 11 +1
2x = 12
x = 6
The measure of angle m∠3 =
5(6) -1
30-1
29º As ∠5 is also congruent then m∠5= 29º
3) ∠1 According to the Vertical Angle Theorem has the same measure as the ∠3, So we can say that ∠1 = 29º
∠2 is supplementary to ∠1
m∠2=180 -29
m∠2=151º
WXYZ is a quadrilateral graphed in the coordinate plane with vertices W(0,5),X(-3,2), Y(0,-4), and Z(3,2). What are the lengths of the sides of the quadrilateral, and what is the correct name for the figure?
Answers
Given: WXYZ is a quadrilateral graphed in the coordinate plane with vertices W(0,5), X(-3,2), Y(0,-4), and Z(3,2).
Required: To determine the side length and type of quadrilateral.
Explanation: The distance between two points is given by the formula-
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The length of side WX is-
[tex]D=\sqrt{(-3-0)^2+(2-5)^2}[/tex]Further solving as-
[tex]\begin{gathered} D=\sqrt{9+9} \\ D=3\sqrt{2}\text{ units} \\ D=4.24\text{ units} \end{gathered}[/tex]Similarly, the side length XY is-
[tex]\begin{gathered} D=\sqrt{(0+3)^2+(-4-2)^2} \\ D=\sqrt{45} \\ D=6.71\text{ units} \end{gathered}[/tex]And, the side length YZ is-
[tex]\begin{gathered} D=\sqrt{(3-0)^2+(2+4)^2} \\ D=\sqrt{45} \\ D=6.71\text{ units} \end{gathered}[/tex]Finally, the side length WZ is-
[tex]\begin{gathered} D=\sqrt{(3-0)^2+(2-5)^2} \\ D=3\sqrt{2} \\ D=4.24\text{ units} \end{gathered}[/tex]Now, since the adjacent sides of the quadrilateral WXYZ are equal, the quadrilateral is a Kite.
Final Answer:
The length of side WX=4.24 units.
The length of side XY=6.71 units.
The length of side YZ=6.71 units.
The length of side ZW=4.24 units.
The best name for this quadrilateral is Kite.
Answer please and thanks
Answers
A percentage of 100 · [p' - exp(- 4000 · k)] / p' of carbon-14 has decayed and lost in last 4000 years.
How to determine the remaining percentage of carbon-14 in ancient pollen
In this question we have the case of simple decay of a radioactive isotope (carbon-14) in time, which is represented by the following exponential formula:
p(t) = p' · exp(- k · t)
Where:
p' - Initial amount of pollen.p(t) - Current amount of pollen.k - Decay constant.t - Time, in years.If we know that t = 4000 years, then percentage of lost carbon-14 is:
p = 100 - 100 · p(t) / p'
p = 100 - [100 · exp(- 4000 · k)] / p'
p = 100 · {1 - [exp(- 4000 · k)] / p'}
p = 100 · [p' - exp(- 4000 · k)] / p'
An amount of 100 · [p' - exp(- 4000 · k)] / p' per cent has been decayed and lost.
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Solve P=3(l+w) for l
Answers
Answer:
l=p/3-w
Step-by-step explanation:
To solve this problem, first distribute.
P=3l+3w
Now, subtract 2w on both sides
p-3w=3l
finally, divide both sides by 3.
3l/3=l
p/3=p/3
-3w/3=-w
The answer would be l=p/3-w
there are 4 swimmers in a race. there will be 1st, 2nd and 3rd place prize awarded. In how many different ways can the prizes be awarded?
Answers
From the problem we will have that:
[tex]\begin{gathered} _4P_3=\frac{4!}{(4-3)!}\Rightarrow_4P_3=\frac{24}{(1)} \\ \\ \Rightarrow_4P_3=24 \end{gathered}[/tex]There will be 24 possible ways to award the 3 prizes between 4 people.
Which best describes the relationship between the lines with equations 4x−8y=9 and 8x−7y=9?A. parallelB. same lineC. neither perpendicular nor parallelD. perpendicular
Answers
The given equations are,
4x-8y=9 and 8x-7y=9
The slopes can be determined as,
[tex]\begin{gathered} m_1=\frac{-a}{b}=\frac{-(4)}{-8}=\frac{1}{2} \\ m_2=\frac{-a}{b}=\frac{-(8)}{-7}=\frac{8}{7} \end{gathered}[/tex]As, the slope are not equal nor their product is -1.
Thus, they are neither parallel nor perpendicular.
Thus, option (C) is correct.
Use f(x) = 4x – 2 and g(x) = 5 – x^2 to evaluate the expression.(a)(f o g)(-2)(b)(g o f)(-2)
Answers
Given the functions:
[tex]\begin{gathered} f(x)=4x-2 \\ g(x)=5-x^2 \end{gathered}[/tex]We will find (f o g)(-2)
So, first, we will find the function (f o g)(x) as follows:
[tex]\begin{gathered} \mleft(f\circ g\mright)(x)=f\lbrack g(x)\rbrack=4(5-x^2)-2 \\ (f\circ g)(x)=20-4x^2-2 \\ (f\circ g)(x)=18-4x^2 \end{gathered}[/tex]Now, substitute with x = -2
so,
[tex](f\circ g)(-2)=18-4\cdot(-2)^2=18-4\cdot4=18-16=2[/tex]so, the answer to the part (a) (f o g)(-2) = 2
b) (g o f)(-2)
We will find (g o f)(x) as follows:
[tex](g\circ f)(x)=g\lbrack f(x)\rbrack=5-(4x-2)^2[/tex]Substitute with x = -2
So,
[tex]\begin{gathered} (g\circ f)(-2)=5-(4\cdot-2-2)^2 \\ =5-(-8-2)^2 \\ =5-(-10)^2 \\ =5-100 \\ =-95 \end{gathered}[/tex]So, the answer to the part (b): (g o f)(-2) = -95
Write an equation that models the linear situation:
A fitness club charges $5 for each class in addition to $150 for the year’s membership.
Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.
For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1
Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.)
To write your equation, use the variables:
n = number of fitness classes attended
C(n) = total cost of fitness club, including classes, for the year (dollars)
Question 2
Write an equation that models the linear situation:
A car rental company charges 5 cents per mile in addition to the base fee of $20.
Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.
For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1
Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.)
To write your equation, use the variables:
m = distance the rental car has been driven (miles)
C(m) = total cost of renting a car (dollars)
Question 3
Write an equation that models the linear situation:
A train starts a trip and it travels at a steady (average) speed of 70 miles per hour.
Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.
For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1
Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.)
To write your equation, use the variables:
t = time traveled (hours)
d(t) = distance traveled (miles)
Write an equation that models the linear situation:
A diver that was 300 feet below the surface of the ocean rises towards the surface 30 feet every minute.
Instructions:
DO NOT USE ANY SPACES between variables, constants, equals signs, and operation signs.
For example, DO NOT enter f(x) = 2x + 1 DO ENTER: f(x)=2x+1
Put parentheses around constants that are fractions like this: y=(2/3)x-(1/2)
You may use decimals IF the decimal values are exact. (You cannot use .33 for 1/3 because it is not exact, but you can use 0.25 for 1/4.)
To write your equation, use the variables:
t = amount of time the diver rises towards the surface (minutes)
L(t) = sea-level position of the diver (feet)
Answers
The linear functions for each case are given as follows:
1. C(n) = 5n + 150.
2. C(m) = 0.05m + 20.
3. L(t) = 30t - 300.
What is a linear function?A linear function, in slope-intercept format, is given by:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).For each item in this problem, we have that the meaning of the coefficients is explained as follows:
The rate per class/mile/rise represents the slope.The initial fees or the initial position represents the intercept.Hence the functions are given as follows, considering the stated variables:
1. C(n) = 5n + 150.
2. C(m) = 0.05m + 20. (5 cents = $0.05).
3. L(t) = 30t - 300. (300 feet below the surface is represented by a negative value, while a rise is represented by a positive value).
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pls help: find the probability of rolling a die five times and getting at least one three
Answers
The probability of getting at least one 3 when a die is rolled 5 times is 0.59 .
What is probability?
The area of mathematics known as probability deals with numerical estimates of how likely an event is to occur.
A die is rolled 5 times.
The sample space is [tex]6^{5}=7776[/tex].
Probability of getting no 5 is [tex]\frac{5}{6}[/tex].
Probability of getting at least one 5 = 1- probability of getting no 5
[tex]1-(\frac{5}{6}) ^{5} \\\\\frac{7776-3125}{7776}\\ \\\frac{4651}{7776}\\ \\0.59[/tex]
Hence Probability of getting at least one 5 is 0.59.
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Check each answer to see whether the student evaluated the expression correctly. If the answer is incorrect cross out the answer and write the correct answer. 6w-19+k when w-8 and k =26(2)-19+8=12-19+8=1
Answers
we have the expression
6w-19+k
Evaluate the given expression for
w=8 and k=2
so
substitute
6(8)-19+2=31
therefore
The answer is incorrect
the correct answer is 31
Assume that there is a 10% rate of disk drive failure in a year.
a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
b. If copies of all your computer data are stored on independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
Answers
The probability that at least one drive is working is 0.99 and the probability that at least one drive is working out of 3 drives is 0.999 .
Probability is the branch of mathematics which deals with the likelihood of an occurrence of an event.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's true probability is a single decimal number between 0 and 1, where, mathematically speaking, 0 denotes the event is impossible and 1 denotes certainty.
Given the probability on one disk failing is 0.1
Probability that both disk fails = 0.1 × 0.1 = 0.01
Now let us calculate the probability that at least one disk does not fail.
We have to find the complement of the above.
Required probability = 1 -0.01 = 0.99
Similarly when 3 independent disc are involved.
Probability that all the disc fails = 0.1 × 0.1 × 0.1 = 0.001
At least one survives = 1 - 0.001 = 0.999
Therefore the probability that at least one drive is working is 0.99 and the probability that at least one drive is working out of 3 drives is 0.999 .
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A particular fruit's weights are normally distributed, with a mean of 406 grams and a standard deviation of 27 grams.The heaviest 14% of fruits weigh more than how many grams?Give your answer to the nearest gram.
Answers
Given
mean of 406 grams and a standard deviation of 27 grams.
Find
The heaviest 14% of fruits weigh more than how many grams?
Explanation
given
mean = 406 gms
standard deviation = 27 gms
using standard normal table ,
[tex]\begin{gathered} P(Z>z)=14\% \\ 1-P(Zso , [tex]\begin{gathered} x=z\times\sigma+\mu \\ x=1.08\times27+406 \\ x=435.16 \end{gathered}[/tex]Final Answer
Therefore , The heaviest 14% of fruits weigh more than 435.16 gms
What are the solutions to the equation 6x2 - x - 40 = 0? A. x = -8/3, x = -5/2B. x = -8/3, x = 5/2 С. x = -2, x = 3 D. x = -6, x = 2
Answers
what is the correct algebraic reprentation for a translation 5 units right and 4 units down?
Answers
We want to write the correct algebraic representation for a translation 5 units right and 4 units down.
Which means 5 units along the positive x axis and 4 units along the negative y axis.
So, we have;
[tex](x,y)\rightarrow(x+5,y-4)[/tex]Therefore, the correct algebraic
help me pleaseeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Solve the formula v = pi r2 h solve for r
Answers
We can do the following steps to solve the given expression for r.
Step 1: We divide by πh from both sides.
[tex]\begin{gathered} v=\pi r^2h \\ \frac{v}{\pi h}=\frac{\pi r^2h}{\pi h} \\ \frac{v}{\pi h}=r^2 \end{gathered}[/tex]Step 2: We apply square root to both sides of the equation.
[tex]\begin{gathered} \sqrt{\frac{v}{\pi h}}=\sqrt{r^2} \\ \sqrt{\frac{v}{\pi h}}=r \end{gathered}[/tex]Answer[tex]r=\sqrt{\frac{v}{\pi h}}[/tex]Describe the set of values that is greater than the quadratic function with zeros –5 and –13 and includes the
point (–9, –32).
Answers
Answer: y>2(x+5)(x+13)
Step-by-step explanation:
edg
Answer:
Answer: y>2(x+5)(x+13)
Step-by-step explanation:
An English teacher at a high school can teach six classes. There are 43 students enrolled in English I, 51 in English II, and 53 in English III. Use the Webster method to determine the apportionment of students to the courses to determine the number of sections needed per course.
Answers
Given:
Heigh school teach = 6 classes
Enrolled student
English 1 = 43
English 2 =51
English 3 =53
Apportionment student is:
[tex]\begin{gathered} =\frac{\text{English}1+\text{English}2+\text{English}3}{6} \\ =\frac{43+51+53}{6} \\ =\frac{147}{6} \\ =24.5 \end{gathered}[/tex]I'm doing topic about classifying numbers can you please help me with these problems?
Answers
According to this question we have to classify what type of number is 10.
The number 10 should be considered as a natural number, real number, rational number, integer number, whole number because of the following reason:
It is a rational and a integer number because because it can be expressed as the quotient of two integers 10/1
Also, it is a natural number because natural numbers are numbers which are used for counting and ordering, and 10 is an example of them.
Also, it is a real number. Real numbers are any number on the real line. So, 10 it is on the real line so, is considered a real number.
Also it is a whole number because it is a natural number.
A train can travel 225 kilometers in 3 hours. At this rate, how many kilometers can the train travel in 7 hours?
Answers
Answer: 1575
Step-by-step explanation: You can multiply 225x7 and you will get 1,575
