By algebra properties, the sum of four mixed numbers is equal to the mixed number [tex]8\,\frac{37}{40}[/tex].
How to simplify a sum of mixed numbers
In this problem we find a sum of four mixed numbers. The simplification process consists in transforming each mixed number into a fraction and apply algebra properties. Then,
[tex]9 \,\frac{1}{2}[/tex] = 9 + 1 / 2 = 18 / 2 + 1 / 2 = 19 / 2
[tex]3\,\frac {7}{8}[/tex] = 3 + 7 / 8 = 24 / 8 + 7 / 8 = 31 / 8
[tex]4\,\frac{4}{5}[/tex] = 4 + 4 / 5 = 20 / 5 + 4 / 5 = 24 / 5
[tex]1 \,\frac{1}{2}[/tex] = 1 + 1 / 2 = 2 / 2 + 1 / 2 = 3 / 2
(19 / 2 - 31 / 8) + (24 / 5 - 3 / 2)
(76 / 8 - 31 / 8) + (48 / 10 - 15 / 10)
45 / 8 + 33 / 10
450 / 80 + 264 / 80
714 / 80
357 / 40
320 / 40 + 37 / 40
8 + 37 / 40
[tex]8\,\frac{37}{40}[/tex]
The sum of mixed numbers is equal to [tex]8\,\frac{37}{40}[/tex].
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Which function has an inverse that is also a function?{(-1 -2). (0, 4). (1 3). (5, 14). (7, 4)}{(-1. 2), (0.4), (1.5). (5. 4). (7.2)} {(-1.3), (0.4). (1. 14), (5. 6). (7. 2)} {-1 4), (04). (1.2). (5.3). (7.1)
Remember that a function is a relation between two sets of numbers where the first set is called domain, and the second set is called range.
The main characteristic that defines a function is that a domain element can be associated with only one element of the range set. In other words, one input value cannot have two different output values.
Therefore, the right answer is the third choice
[tex]\left\lbrace (-1,3\right)(0,4)(1,14)(5,6)(7,2)\}[/tex]Because this represents a function and its inverse also represents a function, that is, it's inverse have the characteristic of a function. The following set represents the inverse
[tex]\left\lbrace (3,-1\right)(4,0)(14,1)(6,5)(2,7)\}[/tex]As you can observe, this inverse set also follows the function definition, because every single input is associated with only one output.
use the point slope formula and the given points to choose the correct linear equation in slope intercept form (0,7) and (4,2)
We have to write the equation of the line that passes through (0,7) and (4,2) in point-slope form.
We start by using the points to calculate the slope m:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-7}{4-0}=-\frac{5}{4}[/tex]Then, if we use point (0,7), we can write the equation in point-slope form as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-7=-\frac{5}{4}(x-0) \\ y=-\frac{5}{4}+7 \end{gathered}[/tex]Answer: the equation is y = -(5/4)*x + 7
Find two functions f and g such that (f O g) (x) =h(x) [tex]h(x) = (9x + 7)^{2} [/tex]
f(x) = x² and g(x) = 9x + 7
Explanation:(fog) (x) = h(x)
h(x) = (9x + 7)²
To get the two functions, we need to understand that the function g(x) will be inserted in function f(x) to get (fog)(x)
g(x) = 9x + 7
This is the function that will be inserted into f(x)
Since we have a square, the function of f(x) will have a square
f(x) = x²
Putting both together, replace x with (9x + 7) in f(x)
(fog)(x) = (9x + 7)²
Hence, f(x) = x² and g(x) = 9x + 7
why is 10'15 equal to 10'11? explain ur thinking. ___ 10'4
Exponent rule is the following:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex][tex]\text{Therefore, if for }\frac{10^{15}}{10^4}\text{ a is 15 and b is 4, therefore:}[/tex][tex]\frac{10^{15}}{10^4}=10^{15-4}[/tex][tex]So,\text{ }10^{\mleft\{15-4\mright\}}=10^{11}[/tex]write a linear equation to: slope=2 and goes through point (4, 11)
When you have to write a linear equation and you have the slope (m) and a point (4, 11) you:
1. Use the standard form of a linear equation:
[tex]y=mx+b[/tex]You know the value of:
m= 2
y= 11
x= 4
You make a substitution:
[tex]11=(2)(4)+b[/tex]You can find then the value of b:
[tex]11=8+b[/tex][tex]b=11-8=3[/tex]Then you have now the data to form the final linear equation:
[tex]y=2x+3[/tex]a large human population of both globally and within individual countries has been a concern since the time of Thomas Malthus. country X is 95% desert. the government of country X is concerned about not having enough arable land (land capable of being used to grow crops) in the country to produce the food needed to feed its population without increasing food imports the demographic for Country X for the year 2020 is provided in the table below. 1. calculate the national population growth rate for a country X 2. using the rule of 70 calculate the doubling time for this population
Firstly, we want to calculate the growth rate of the population
While birth would increase the population, death and migration will decrease the population
So when we subtract the migration rate and the death rate from the birth rate, we can get the population growth rate;
Thus, we have;
[tex]\begin{gathered} \frac{38}{1000}\text{ - (}\frac{24}{1000}\text{ + }\frac{2}{1000}) \\ \\ =\text{ }\frac{38}{1000}\text{ - }\frac{26}{1000} \\ \\ =\text{ }\frac{12}{1000} \end{gathered}[/tex]The national population growth rate for a country X is 12/1000
Secondly, we are to use the rule of 70 to calculate the doubling time for the population
Mathematically;
[tex]\begin{gathered} No\text{ of years to double = }\frac{70}{\text{annual growth rate}} \\ \\ No\text{ of years to double = 70 divided by }\frac{12}{1000} \\ \\ No\text{ of years = 70 }\times\frac{1000}{12}=5833\frac{1}{3}years^{} \\ \\ \frac{1}{3}\text{ years is same as 4 months} \\ \\ So\text{ it will take 5833 years and 4 months for the population to double} \end{gathered}[/tex]Hello, may I please have some help with this question. Thank you.
The total distance that Kim walked in 3 days is 6 2/3 miles. We would convert this distance to mixed numbers. To do this, we would multiply 6 by 3 and add 2. The denominator would still be 3. It becomes
20/3 miles
If she walked 20/3 miles in 3 days, the number of miles that she walked per day would be
total distance/number of days
It becomes
(20/3) / 3
If we change the division sign to multiplication, it means that we would flip 3 such that it becomes 1/3. Thus, we have
20/3 * 1/3 = 20/9
= By converting to mixed numbers, we would find how many 9's are in 20. It is 2. The remainder is 20 - 18 = 2
Thus, the answer is
2 2/9 miles per day
use the half angle identity to find the exact value of the trigonomic expression. given 0
Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
Use the graphs below to help you answer the question.
Which of the following is the best approximation to a solution of the equation e* = 4x+1?
A. 10
B. 2
C. 3
D. 1
Answer:
I would say the answer is D.
Step-by-step explanation:
If you solve for x you get 1/4.
In decimal form that is 0.4
Suppose a normal distribution has a mean of 98 and a standard deviation of6. What is P(x < 110)?A. 0.84B. 0.16C. 0.025O D. 0.975
We know that
• The mean is 98.
,• The standard deviation is 6.
,• The given x-value is 110.
First, we find the z-value using the following formula
[tex]Z=\frac{x-\mu}{\sigma}_{}[/tex]Replacing the given information, we have
[tex]Z=\frac{110-98}{6}=\frac{12}{6}=2_{}[/tex]The z-value or z-score is 2.
Then, we use a z-table to find the probability when P(x<110), or P(z<2).
We obtain a probability of 0.97, which approximates to D.
Hence, the probability would be D.I wanted to know if this is the right answer
Notice that angles 6 and 4 are alternate exterior angles, therefore:
[tex]m\measuredangle4=m\measuredangle6.[/tex]Answer: m<4=66.
are these places correctly.and yes it is math. pls answer fast
we have that
Costs that stay the same from week to week or month to month
-savings for college
-Rent
Costs that cannot be adjusted within a budget
-Car insurance
-Health care
Costs that can be adjusted within a budget
-cell phone
-gasoline
-hair cut
-Groceries
Evaluate each function. Be sure to show your substitutions.h(x) = 7x^2 - 4x-15h(20)
The function is given as,
[tex]h(x)=7x^2-4x-15[/tex]The objective is to determine the value h(20).
This can be obtained by substituting 20 for 'x' in the given expression,
[tex]\begin{gathered} h(20)=7(20)^2-4(20)-15 \\ h(20)=7(400)-80-15 \\ h(20)=2800-95 \\ h(20)=2705 \end{gathered}[/tex]Thus, the value of the given function h(20) is 2705.
ExpenseYearly costor rateGasInsuranceWhat is the cost permile over the course ofa year for a $20,000 carthat depreciates 20%,with costs shown in thetable, and that hasbeen driven for 10,000miles?$425.00$400.00$110,00$100.0020%OilRegistrationDepreciationB. $4.10 per mileA. $1.10 per mileC. $0.25 per mileD. $0.50 per mile
Step 1:
Find the depreciation
[tex]\begin{gathered} \text{Depreciation = 20\% of \$20,000} \\ \text{Depreciation = }\frac{20}{100}\text{ }\times\text{ \$20000} \\ \text{Depreciation = \$4000} \end{gathered}[/tex]Step 2:
Total cost = $425 + $400 + $110 + $100 + $4000
Total cost = $5035
Final answer
[tex]\begin{gathered} \text{Cost per mile = }\frac{5035}{10000} \\ \text{Cost per mile = \$0.5035} \\ \text{Cost per mile = \$0.50} \end{gathered}[/tex]Option D $0.50 per mile
What is the gcf of 16 and 28
Answer:
4
Step-by-step explanation:
What’s the correct answer answer asap for brainlist
Answer: serbia
Step-by-step explanation:
What is the solution of the system of equations? Explain.18x+15-y=05y=90x+12
The given system is
[tex]\begin{cases}18x+15-y=0 \\ 5y=90x+12\end{cases}[/tex]First, we multiply the first equation by 5.
[tex]\begin{cases}90x+75-5y=0 \\ 5y=90x+12\end{cases}[/tex]Then, we combine the equations
[tex]\begin{gathered} 90x+75-5y+5y=90x+12 \\ 90x+75=90x+12 \\ 75=12 \end{gathered}[/tex]Given that the result is not true (75 is not equal to 12), we can deduct that the system has no solutions.
Louis food out six different size at the picnic at the end of the picnic he noticed this about about the pies one whole apple pie was eaten and 3/4
Louis had 6 different pies. Some of them were eating and we want to know how much pie there's left. First, we have the information that one apple pie was entirely gone. From this, we know there were 5 pies remaining.
[tex]6-1=5[/tex]Then, he also noticed the other apple pie had 3/4 gone. Which means that 1/4 of this second apple pie was leftover.
[tex]1-\frac{3}{4}=\frac{1}{4}[/tex]Applying this same logic, we can deduct all the slices that were eaten from the total amount of pie we had at first to get the leftovers.
[tex]\begin{gathered} 6-1-\frac{3}{4}-\frac{1}{2}-\frac{1}{8}-\frac{5}{8}-\frac{3}{4} \\ =5-\frac{1}{2}-\frac{6}{4}-\frac{6}{8} \\ =5-2-\frac{3}{4} \\ =3-\frac{3}{4} \\ =2+\frac{1}{4} \end{gathered}[/tex]What we've done in this last equation, was taking our first amount of pies (6), subtract the whole apple pie that was eaten (1), the three quarters that were eaten from the other apple pie (3/4) and the other eaten slices from the others.
Which means, the result of this calculation is our amount of leftover slices.
We still have 2 and a quarter pies.
The lengths of two sides of the right triangle ABC shown in the illustration givena=12 cm and c= 20cm
In the right triangle of sides a, b, and c
[tex]a^2+b^2=c^2[/tex]Since a = 12 and c = 20
Substitute them in the given rule
[tex]\begin{gathered} (12)^2+b^2=(20)^2 \\ 144+b^2=400 \end{gathered}[/tex]Subtract 144 from both sides
[tex]\begin{gathered} 144-144+b^2=400-144 \\ b^2=256 \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sqrt[]{b^2}=\sqrt[]{256} \\ b=16 \end{gathered}[/tex]The answer is b = 16
Mike made $120 last week working d days. Express the amount he made each day in terms of d.
Since he made $120 in d days
To find his earn in eac
8+7t=22 in verbal sentence
Eight plus Seven times t equals twenty-two
Explanation
Step 1
Let
a number= t
seven times a number= 7t
the sum of eigth and seven times a number=8+7t
the sum of eigth and seven times a number equals twenty-two=8+7t=22
or,in other words
Eight plus Seven times t equals twenty-two
I hope this helps you
In the accompanying diagram of circle O, COA is adiameter, O is the origin, OA = 1, and mLBOA = 30. Whatare the coordinates of B?
Given:
COA is a diameter
O is the origin
OA = 1
m< BOA = 30
Re-drawing the diagram to show the coordinates of the B:
Let the coordinates of B be (x,y)
Using trigonometric ratio, we can find the length of side AB
From trigonometric ratio, we have:
[tex]tan\text{ }\theta\text{ = }\frac{opposite}{adjacent}[/tex]Substituting we have:
[tex]\begin{gathered} tan\text{ 30 = }\frac{y}{1} \\ Cross-Multiply \\ y\text{ = tan30 }\times\text{ 1} \\ y\text{ = 0.577} \\ y\text{ }\approx\text{ 0.58} \end{gathered}[/tex]Hence, the coordinates of B is (1, 0.58)
A couple of friends decide to race each other. Emmet can run 6 yards per second, whereas Ayana can run 9 yards per second. Because he is slower, Emmet also gets a head start of 30 yards. Shortly after they start running, Ayana will catch up to Emmet. How far will Ayana have to run?Write a system of equations, graph them, and type the solution.
We know the formula d=rt where d is distance, r is rate and t is time
Emmet:
d = 6 yd/s * t
Ayana:
d = 9 yd/s * t
We give Emmet 30 less yards to run
Emmet:
d - 30 = 6 yd/s * t
d = 6t + 30
Setting the equations equal to each other
9 * t = 6t + 30
Subtract 6t from each side
9t-6t = 30
3t = 30
Divide by 3
3t/3 = 30/3
t = 10 seconds
It will take 10 seconds for Ayana to catch up
Ayana:
d = 9 yd/s * t
d = 8 * 10 = 90 yds
QUESTION 31 POINTThe area of a triangle is 18. The base is 6 inches. What is the height? Do not include units in your answer.
ANSWER:
6
STEP-BY-STEP EXPLANATION:
The area of a triangle is given by the following equation:
[tex]A=\frac{b\cdot h}{2}[/tex]We replace and solve for h (height)
[tex]\begin{gathered} 18=\frac{6\cdot h}{2} \\ h=\frac{18\cdot2}{6} \\ h=6 \end{gathered}[/tex]The height of the triangle is 6 inches
help meeeeeeeeee pleaseee !!!!!
The values of the functions are:
a. (f + g)(x) = 9x + 1
b. (f - g)(x) = -7x - 17
c. (f * g)(x) = 8x² - 55x - 72
d. (f/g)(x) = (x - 8)/(8x + 9)
How to Evaluate Functions?To evaluate a function for a given value of input, substitute the value of the input, x, into the function equation, evaluate and simplify.
Given the following:
f(x) = x - 8
g(x) = 8x + 9
a. (f + g)(x) = (x - 8) + (8x + 9)
Combine like terms
(f + g)(x) = 9x + 1
b. (f - g)(x) = (x - 8) - (8x + 9)
(f - g)(x) = x - 8 - 8x - 9
Combine like terms
(f - g)(x) = -7x - 17
c. (f * g)(x) = (x - 8)(8x + 9)
Expand
(f * g)(x) = x(8x + 9) -8(8x + 9)
(f * g)(x) = 8x² - 55x - 72
d. (f/g)(x) = (x - 8)/(8x + 9)
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A window washer drops a tool from their platform 155 ft high. The polynomial -16r2 + 155 tells us the height, in feet, of
the tool / seconds after it was dropped. Find the height, in feet, after t = 1.5 seconds.
At t = 1.5 sec the tool is at the height of 119 feet.
Given, A window washer drops a tool from their platform 155 ft high.
The polynomial -16r² + 155 tells us the height, in feet, of the tool / seconds after it was dropped.
we are asked to determine the height, in feet, after t = 1.5 seconds.
we know that h(t) = -16r² + 155
hence at t=1.5 sec, height is = ?
⇒ h(1.5) = -16t² + 155
⇒ h(1.5) = -16(1.5)² + 155
⇒ h(1.5) = -16(2.25) + 155
⇒ h(1.5) = -36 + 155
⇒ h(1.5) = 119
at t=1.5 sec the tool is at the height of 119 feet.
Hence we get the height as 119 feet.
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What is the value of 3÷5?
Answer:
0.6
Step-by-step explanation:
End Behavior Graphically
We will investigate how to determine the end behaviours of polynomial functions.
The function given to us is:
[tex]f(x)=123x^3+9x^4-786x-3x^{5^{}}-189x^2\text{ + 1260}[/tex]Whenever we try to determine the end-behaviour of any function. We are usually looking for value of f ( x ) for the following two cases:
[tex]x\to\infty\text{ and x}\to-\infty[/tex]The most important thing to note when dealing with end-behaviour of polynomial functions is that the behaviour is pre-dominantly governed by the highest order term of a polynomial. The rest of the terms are considered small or negligible when considering end-behaviours of polynomials.
The highest order terms in the given function can be written as:
[tex]f(x)=-3x^5[/tex]Then the next step is to consider each case for the value of ( x ) and evaluate the value of f ( x ) respectively.
[tex]\begin{gathered} x\to\infty \\ f\text{ ( }\infty\text{ ) = -3}\cdot(\infty)^5 \\ f\text{ ( }\infty\text{ ) = -3}\cdot\infty \\ f\text{ ( }\infty\text{ ) = -}\infty \end{gathered}[/tex]Similarly repeat the process for the second case:
[tex]\begin{gathered} x\to-\infty \\ f\text{ ( -}\infty\text{ ) = -3}\cdot(-\infty)^5 \\ f\text{ ( -}\infty\text{ ) = 3}\cdot\infty \\ f\text{ ( -}\infty\text{ ) = }\infty \end{gathered}[/tex]Combining the result of two cases we get the following solution:
[tex]As\text{ x}\to\text{ }\infty\text{ , y}\to\text{ -}\infty\text{ and as x}\to-\infty\text{ , y}\to\text{ }\infty[/tex]Correct option is:
[tex]\text{Option C}[/tex]Determine the frequency of each class and the table shown
Given:
The dataset and table with class.
Required:
Determine the frequency of each class.
Explanation:
Answer:
Answered the question.
What is the value of f(-5) in the piecewise function -3x + 1 when x > 1 f(x) = -2x when x = 1 2x - 1 when x < 1
Answer:
f(-5)=-11
Explanation:
Given the piecewise function:
[tex]f(x)=\begin{cases}{-3x+1,\text{ when }x>1} \\ {-2x,\text{ when }x=1} \\ {2x-1,\text{ when }x<1}\end{cases}[/tex]We want to find the value of f(-5).
When x=-5:
[tex]\begin{gathered} -5<1\implies f(x)=2x-1 \\ \text{ Therefore:} \\ f(-5)=2(-5)-1 \\ =-10-1 \\ =-11 \end{gathered}[/tex]The value of f(-5) is -11.
