Let b be the number of students that were in each bus, since 111 students were on the trip, 23 students rode in cars, and the rest filled 4 buses, then we can set the following equation:
[tex]111=23+4b\text{.}[/tex]Subtracting 23 from the above equation we get:
[tex]\begin{gathered} 111-23=23+4b-23, \\ 88=4b\text{.} \end{gathered}[/tex]Dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{88}{4}=\frac{4b}{4}, \\ b=22. \end{gathered}[/tex]Answer: 22 students.
The mean of the data set shown in the table is 57. What is the mean absolute deviation?699.512
To find the mean absolute deviation of the data set, first, you have to calculate the absolute value of the difference between each value of the data set and the mean.
The data set is
[tex]\mleft\lbrace6,9,9.5,12\mright\rbrace[/tex]The mean of the data set is 57
This relation is a function:{(5,-2), (6,-2),(7,-2), (8,-2)}A.TrueB.False
Danielle is trying to solve the equation 25^x+3=176 Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Given:
Equation is:
[tex]\begin{gathered} 25^x+3=176 \\ \end{gathered}[/tex]Find-:
Solve the equation
Explanation-:
Simplify the equation then,
[tex]\begin{gathered} 25^x+3=176 \\ \\ 25^x=176-3 \\ \\ 25^x=173 \\ \\ 5^{2x}=173 \end{gathered}[/tex]Taking ln both sides then,
[tex]\ln5^{2x}=\ln173[/tex]Use logarithmic property
[tex]\ln a^b=b\ln a[/tex]Then the value is:
[tex]\begin{gathered} \ln5^{2x}=\ln173 \\ \\ 2x\ln5=\ln173 \\ \\ 2x=\frac{\ln173}{\ln5} \\ \\ x=\frac{\ln173}{2\ln5} \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} x=\frac{\ln173}{2\ln5} \\ \\ x=\frac{5.1533}{2\times1.6094} \\ \\ x=\frac{5.1533}{3.2189} \\ \\ x=1.601 \end{gathered}[/tex]So, the value of "x" is 1.601
as many. How many successful free throws did Priya make today?
free throws
vitamin C (mg)
25%
0
50%
0
75%
2.
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C,
which is 250% of the daily recommended allowance of vitamin C for adults. What is
100% of the daily recommended allowance of vitamin C for adults?
10000
100%
1500
125%
150%
20006
25006
Answer:
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?
Matthew drives 54 miles per hour. Benjamin drives 47 miles per hour. They started at the same spot, and drove in opposite directions. Aftersome time, they were 1272.6 miles apart. How much time has passed?After _____ hours, Matthew and Benjamin were 1272.6 miles apart.
Solution:
Matthew and Benjamin start from the same spot and drives in opposite directions.
Given:
[tex]\begin{gathered} \text{Matthew's sp}eed=54mph \\ \text{Benjamin's sp}eed=47mph \\ \text{Distance apart after time (t)=1272.6miles} \end{gathered}[/tex]The formula for speed is given by;
[tex]\begin{gathered} \text{Speed}=\frac{dis\tan ce}{\text{time}} \\ \text{Hence, } \\ \text{distance}=\text{speed}\times time \end{gathered}[/tex]During the journey, they used the same time but moved at different speeds, hence, they will have different distances.
Let the time both used be represented by t
Let Matthew's distance be represented by m
Let Benjamin's distance be represented by b
Thus,
Matthew's distance is calculated below;
[tex]\begin{gathered} \text{distance}=\text{speed}\times time \\ m=54\times t \\ m=54t \end{gathered}[/tex]Benjamin's distance is calculated below;
[tex]\begin{gathered} \text{distance}=\text{speed}\times time \\ b=47\times t \\ b=47t \end{gathered}[/tex]The distance covered by the two of them in opposite directions is their distance apart from the starting point.
Hence,
[tex]m+b=1272.6[/tex][tex]\begin{gathered} 57t+47t=1272.6 \\ 101t=1272.6 \\ \text{Dividing both sides by 101 to get the time t,} \\ t=\frac{1272.6}{101} \\ t=12.6\text{hrs} \end{gathered}[/tex]Therefore, after 12.6hours, Matthew and Benjamin were 1272.6 miles apart.
Rendering math...Five adults and four children go to the museum. They pay a total of $19 for admission. Theadult admission fee is three times the fee for a child. If an adult ticket costs x dollars and a ticket for a childcosts y dollars, which of the following statements are correct? Select all that apply.One of the equations to be used in solving the problem is x=3y.After a possible substitution, 53y+4y=19 can be obtained.One of the equations to be used in solving the problem is y=3x.After a possible substitution, 53x+4x=19can be obtainedThe adult fee is 3 dollars.The ticket for a child costs 2 dollars.5One of the equations to be used in solving the problem is x=3y.After a possible substitution, 53y+4y=19 can be obtained.One of the equations to be used in solving the problem is y=3x.After a possible substitution, 53x+4x=19can be obtained.The adult fee is 3 dollars.English (US)ere to searchE1515 +G
Let be "x" the cost in dollars of an adult ticket and "y" the cost in dollars of a child ticket.
You know that a 5 adults and 4 children went to the museum and the total cost was $19. Therefore, you can write the following equation:
[tex]5x+4y=19[/tex]The word "Three times" indicates a multiplication by 3. Therefore, "The
adult admission fee is three times the fee for a child" can be written as:
[tex]x=3y[/tex]In order to find the values of "x" and "y", substitute the second equation into the first one and solve for "y":
[tex]\begin{gathered} 5(3y)+4y=19 \\ 15y+4y=19 \\ 19y=19 \\ y=1 \end{gathered}[/tex]To find "x", substitute the value of "y" into the second equation. Then:
[tex]\begin{gathered} x=3(1) \\ x=3 \end{gathered}[/tex]Therefore, you can identify that the correct options are:
- One of the equations to be used in solving the problem is :
[tex]x=3y[/tex]- The adult fee is 3 dollars.
Brianna is buying a house for $210,000. She plans to make a 14% down payment. Closing costs include $650 for 6 months of homeowners insurance, $600 for 6 months of property tax, $125 for the title fee, and $350 in transaction fees. Brianna also agreed to pay two points in exchange for a 0.5% reduction in interest rate. Determine the amount of money Brianna needs to cover closing costs. Round your answer to the nearest cent.
2102 subscript 3 + 1001 subscript 3
Answer:
[tex]10110_3[/tex]Explanation:
Given the sum:
[tex]2102_3+1001_3[/tex]The sum (in base 3) is evaluated below:
The answer is 10110 (in base 3).
X
-1
0
1
3
Y
10
7
4
-2
find the slope and y-intercept
m =
b =
Slope of the line is - 3 and y-intercept is 6
Slope - intercept form of line is y = mx + b where m is slope of the line and b is intercept on y-axis
taking any two points from the table
A(-1 ,10) , B(0,7)
calculating slope by y₂-y₁/x₂-x₁
putting x₁ = -1 , x₂ = 10 and y₁ =0 , y₂=7
m = 7-10 / 0 + 1 = -3/1
m = -3
equation of line will be y = -3x + b
calculating intercept b by putting one point in equation of line
10 = -3(-1) + b
10 = 4 + b
b = 6
substituting value of b in the equation
y = -3x + 6 is our equation of line
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Write the equation of the line that passes through the points (8, -1) and (2, -5) inpoint-slope form.
First, we find the slope using the given points and the formula below
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-5-(-1)}{2-8}=\frac{-5+1}{-6}=\frac{-4}{-6}=\frac{2}{3}[/tex]Then, we use the point-slope formula to find the equation
[tex]y-y_1=m(x-x_1)_{}[/tex]Let's replace the point (8, -1) and the slope 2/3.
[tex]\begin{gathered} y-(-1)=\frac{2}{3}(x-8) \\ y+1=\frac{2}{3}x-\frac{16}{3} \\ y=\frac{2}{3}x-\frac{16}{3}-1 \\ y=\frac{2}{3}x+\frac{-16-3}{3} \\ y=\frac{2}{3}x-\frac{19}{3} \end{gathered}[/tex]Hence, the equation in point-slope form is[tex]y+1=\frac{2}{3}(x-8)[/tex]4. Maliyah has 3 54 cups of dough for baking bread. Each loaf of bread requires96 of a cup of dough. What is the exact number of loaves that Maliyah canmake from the dough?
Write 3 3/4 as a fraction:
[tex]3\frac{3}{4}=3+\frac{3}{4}=\frac{12}{4}+\frac{3}{4}=\frac{15}{4}[/tex]Use conversion factor to find the exact number of loaves that Maliyah can make with 3 3/4 (15/4) cups of dough.
1 loaf requires 1/6 of cup of dough.
[tex]\frac{15}{4}\text{cups}\cdot\frac{1\text{loaf}}{\frac{1}{6}\text{cup}}=\frac{15}{4}\text{cups}\cdot6\frac{\text{loaf}}{\text{cup}}=\frac{90}{4}\text{loaves}=\frac{45}{2}\text{loaves}[/tex]You can write the answer as a mixed number:
[tex]\frac{45}{2}=\frac{44}{2}+\frac{1}{2}=22\frac{1}{2}[/tex]Then, with 3 3/4 cups of dough Maliyah can make 22 1/2 (45/2) loaves of bread.
A medical clinic has a crew of 5, two of which have been infected with a virus althoughthey show no symptoms. If you select two crew members for a task, what is the probability that there is at least one infected person in group assigned for the task.
P(at least 1 infected person) = 0.7
Explanation:Note that:
Probability = (Number of possible outcomes) / (Number of total outcomes)
The crew members = 5
Number of infected crew members = 2
Number of uninfected crew members = 3
We want to select two crew members for a task out of 5
Number of total outcomes = 5C2 (Selecting 2 out of 5)
Note that:
[tex]nCr=\frac{n!}{(n-r)!r!}[/tex][tex]\begin{gathered} 5C2=\frac{5!}{(5-2)!2!} \\ \\ 5C2=\frac{5!}{3!2!} \\ \\ 5C2=\frac{5\times4\times\cancel{3!}}{\cancel{3!}\times(2\times1)} \\ \\ 5C2=\frac{20}{2} \\ \\ 5C2=10 \end{gathered}[/tex]Number of total outcomes = 10
That is, there are 10 ways of selecting 2 crew members from 5
Number of ways of selecting 1 infected person means how we can select two people out of 5 such that 1 one of them will be infected. This means that we will select 1 from the two infected persons, and select the second one from the 3 uninfected persons
Number of ways of selecting 1 infected persons = 2C1 x 3C1
[tex]\begin{gathered} 2C1=\frac{2!}{(2-1)!1!}=\frac{2!}{1!1!}=\frac{2\times1}{1\times1} \\ 2C1=2 \\ \\ 3C1=\frac{3!}{(3-1)!1!}=\frac{3!}{2!1!}=\frac{3\times2\times1}{2\times1\times1}=\frac{6}{2} \\ 3C1=3 \end{gathered}[/tex]Number of ways of selecting 1 infected persons = 2 x 3
Number of ways of selecting 1 infected persons = 6
Number of ways of selecting 2 infected persons = 2C2
[tex]2C2=\frac{2!}{(2-2)!2!}=\frac{2!}{2!}=1[/tex]Number of ways of selecting 2 infected persons = 1 way
Probability of selecting 1 infected person = 6/10 = 0.6
Probability of selecting 2 infected person = 1/10 = 0.1
P(at least 1 infected person) = P(1 infected person) + P(2 infected persons)
P(at least 1 infected person) = 0.6 + 0.1
P(at least 1 infected person) = 0.7
On a coordinate plane, PQ is translated 3 units up and 3 units to the right to create P'Q'. Line p is drawn through P and P', and Line q is drawn through Q and Q'. Which
statement about Lines p and q is true?
O Lines p and q are parallel.
O Lines p and q are perpendicular.
O Lines p and a have the same x-intercept.
Lines p and a have the same y-intercept.
The correct statement about line p and q is, Lines p and q are parallel.
What is translation of graph?
Any movement of the graph either horizontally or vertically parallel to the -axis is referred to as a translation.
In mathematics, a translation is the movement of a shape left, right, up, or down. The translated shapes are identical to the original ones in size, indicating that they are congruent. They simply changed positions in one or more directions. The shape is unchanged because it is simply being transferred from one location to another.
Let, On a coordinate plane, PQ is translated 3 units up and 3 units to the right to create P'Q'. Line p is drawn through P and P', and Line q is drawn through Q and Q'.
There is no change in the shape or size of p and q.
Hence, lines p and q are parallel.
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can you please completely factor [tex]11 {x}^{2} + 24x + 1320[/tex]
There are 16 ounces in 1 lb juwan is mailing a package that weighs 10 lb he wants to know the weights of the package and the ounces
Juwan is mailing a package that weighs 10lb
for every 1 lb you have 16 ounces inside the package
if 1 lb ------- 16 ounces
10lb ------- x ounces
reason why we have x ounces is because we dont know how many ounces 10 lb we give us
cross multiplication
1 * x = 10 x 16
x = 10 x 16
x = 160 ounces
10lb we give us a total of 160 ounces
therefore, there are 160 ounces in the 10 lb package juwan is mailing
The answer is 160 ounces
9. Use the figure shown to identify each.
a. Vertical angles
b. Adjacent angles
c. Linear pairs
d. Supplementary angles
e. Complementary angles
Answer:
Step-by-step explanation:
For some of the questions there are multiple answers that could be correct. Here’s some of the possible answers. Hope that helps!
a. 3 & 5
b. 3 & 4
c. 4 & 5
d. 4 & 5
e. 1 & 2
In two days, Mariposa drinks seven 16-ounce
bottles of water. She drinks the water in 4 equal
servings. How many ounces of water does
Mariposa drink in each serving?
Answer:
28 oz
Step-by-step explanation:
First, find the total amount of water that was drank.
7 × 16 oz = 112 oz total
Then, divide this by 4 to get the amount per one serving.
112 oz / 4 = 28 oz per serving
PLEASE HELP!!!
A line passes through the point (4, 8) and has a slope of 3/2.
Write an equation in slope-intercept form for this line.
Answer:
y=1.5x+2
Step-by-step explanation:
The equation for a line in slope-intercept form is written as y=mx+c where m is the slope and cis the y-intercept.
We know the slope is 3/2 or 1.5, so we can write
y=1.5x+c
We know the line contains the point (4,8), so we can sub this in to find c:
8=1.5(4)+c
8=6+c
c=2
Having found m and c, we can write the equation:
y=1.5x+2
Answer: [tex]\text{y}=\frac{3}{2}\text{x}+2\\\\[/tex]
This is the same as writing y = (3/2)x + 2
=====================================================
Work Shown:
[tex]\text{y}-\text{y}_1=\text{m}\left(\text{x}-\text{x}_1\right)\\\\\text{y}-8=\frac{3}{2}\left(\text{x}-4\right)\\\\\text{y}-8=\frac{3}{2}\text{x}+\frac{3}{2}(-4)\\\\\text{y}-8=\frac{3}{2}\text{x}-6\\\\\text{y}=\frac{3}{2}\text{x}-6+8\\\\\text{y}=\frac{3}{2}\text{x}+2\\\\[/tex]
I used point-slope form as the first step. The 'm' is the slope, and [tex](x_1,y_1) = (4,8)[/tex] is the point on the line.
The final step shows us the line has a y intercept of b = 2, which is at the location (0,2).
To graph this, draw a straight line through (0,2) and (4,8)
--------------
Check:
Plug x = 4 into the equation we found. We should arrive at y = 8.
[tex]\text{y}=\frac{3}{2}\text{x}+2\\\\\text{y}=\frac{3}{2}*4+2\\\\\text{y}=\frac{12}{2}+2\\\\\text{y}=6+2\\\\\text{y}=8\\\\[/tex]
This confirms (4,8) is indeed on this line and confirms the answer is correct.
You can also use graphing tools like Desmos or GeoGebra to quickly and visually confirm the answer.
How do I find the feet in a 9 inch board
Answer:
3/4 of a foot.
Step-by-step explanation:
In order to find how many feet are in 9 inches, we simply divide 9 by 12. We use the number 12, because that is how many inches are in a foot. 9 divided by 12 = 0.75 or 3/4 of a foot.
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
which angle is congruent to
The angle congruent to ∠CGD is the angle ∠AGF as they are vertical angles.
A school assembly had 40 students in attendance, and 80% of them were first-graders. How many first-
graders were at the assembly?
Answer: 32 first graders were at the assembly
Step-by-step explanation:
80% of 40 can be written as 80% × 40
= 80/100 × 40
= 32
Thus, 80% of 40 is 32.
is shape A congruent to shape 82BA
Solution
For this case the answer would be:
yes
And the reason is because we have the same shape and with the smae structure so then are congruent
It takes `20` tomato slices to make `2` of Ivan's pizzas.
How many does it take to make 10 pizzas?
Answer:
100
Step-by-step explanation:
If you need 20 for every 2 pizzas, that means you would need 10 for 1 pizza. (tomato's) 10 x (pizzas)10 = 100
pls tell the answer pls plsplsplsplsplspls
a) 20 people travel more than 30 miles to work.
b) Sam travels 20 miles .
Given,
In the question:
From the graph:
The histogram shows information about how 550 people travel to work.
To find the how many people travel more than 30 miles to work?
Now, According to the question:
Observe the Graph :
a) How many people travel more than 30 miles to work
5 x 4 = 20 people
b) 205 of the 550 people travel further than Sam . Estimate how far Sam travel?
Now, According to the question:
205 of the 550 people travel further than Sam,
Sam travels 20 miles .
Hence, a) 20 people travel more than 30 miles to work.
b) Sam travels 20 miles .
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The function B(t) 17,550(0.88) models the value of a boat. t years after it was purchased. Which statement is true about the value of the boat? A The value of the boat is increasing by 12% each year. B. The value of the boat is increasing by 88% each year. C. The value of the boat is decreasing by 12% each yearD. The value of the boat is decreasing by 88% each year.
Answer:
Explanation:
The function that models the value of the boat is given as:
[tex]B\mleft(t\mright)=17,550\mleft(0.88\mright)^t[/tex]We can rewrite this as:
[tex]B(t)=17,550(1-0.12)^t[/tex]This is in the form of an exponential decay
You have 26 video games in your collection.Some are for the X-Box system and someare for PlayStation. You have 4 fewerPlaystation games than X-Box games.Write a variable expression to model thesituation. How many of each type of gamedo you have?
Total number of videogames = 26
PLaystation games = y
x box games = x
x+y=26
You have 4 fewer (-4) PlayStation games than X-Box games.
y = x-4
The system is:
x+y=26 (a)
y = x-4 (b)
Puy (b) into (a)
x+ (x-4) =26
x+x-4 =26
Solve for x:
2x= 26+4
2x=30
x=30/2
x=15 (c)
(c) into (b)
y=15-4
y=11
X box games = 15
Playstation games = 11
what is one important difference between a normal distribution and a t distribution? group of answer choices the t distribution has heavier tails than a normal distribution. the normal distribution has heavier tails than a t distribution. the two distributions have similar tails, it's just that the t distribution can be skewed, while the normal distribution may not be skewed.
The t distribution has heavier tails than a normal distribution. the normal distribution has heavier tails than a t distribution. the two distributions have similar tails, it's just that the t distribution can be skewed, while the normal distribution may not be skewed.
There are a few important differences between a normal distribution and a t distribution. First, the t distribution has heavier tails than the normal distribution. This means that there is a greater chance of observing extreme values in the t distribution. Second, the t distribution can be skewed, while the normal distribution may not be. This means that the t distribution is more likely to have values that are not evenly distributed around the mean. Finally, the t distribution is more variable than the normal distribution. This means that the t distribution is more likely to have values that are far from the mean.
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The owner of Rockport Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 11 small arrangements and 1 large arrangement, which took her a total of 62 minutes. After lunch, she arranged 12 small arrangements and 1 large arrangement, which took 67 minutes. How long does it take to assemble each type?
To solve this, we need to write a system of equations.
We know that it took her 62 minutes to assemble 11 small and 1 large.
Let's call the small arrangements S, and the large L.
Then:
[tex]11S+L=62[/tex]After lunch, she did 12 small and 1 large in 67 minutes. Then:
[tex]12S+L=67[/tex]Now we have the system of equations:
[tex]\begin{cases}11S+L=62 \\ 12S+L=67\end{cases}[/tex]To solve by elimination, we need to eliminate one unknown by adding or substracting the two equations. If we rest the first equation to the second equation:
[tex](12S+L)-(11S+L)=67-62[/tex]Now we can solve:
[tex]\begin{gathered} 12S-11S+L-L=65-62 \\ S=5 \end{gathered}[/tex]To make a small arrangement takes her 5 minutes. Now we can go back to the first equation and replace S = 5:
[tex]\begin{cases}11S+L=62 \\ S=5\end{cases}\Rightarrow11\cdot5+L=62[/tex]And solve for L:
[tex]\begin{gathered} 55+L=62 \\ L=62-55 \\ L=7 \end{gathered}[/tex]Then it takes her 7 minutes to make a large arrangement.
To change a fraction into a decimal do you, divide the denominator by the numerator.
To change a fraction into a decimal do you, divide the denominator by the numerator. FALSE. You should divide the numerator by the denominator (the top by the bottom).
Answer:
No.
You divide the numerator by the denominator.
Step-by-step explanation:
No.
You divide the numerator by the denominator.
For example, 8/2 = 8 divided by 2 = 4
1/5 = 1 divided by 5 = 0.2
For the following exercise, write a formula for the function g that results when the graph of a given toolkit function is transformed as described.
The graph of f(x)=1/x is vertically stretched by a factor of 5 units, then shifted to the right 2 units and up 6 units.
g(x)=
The required transformed function is given by, g(x) = 5/(x-2) + 6
Given the parent function is, f(x) = 1/x
Now if we vertically stretched the function by a factor 5 units then the function becomes,
g(x) = 5/x
Again if we shifted to the right to 2 units then the function becomes,
g(x) = 5/(x-2)
Further if we shift up to 6 units then the function transformed to,
g(x) = 5/(x-2) + 6
Hence the ultimate transformed function is, g(x) = 5/(x-2) + 6.
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