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
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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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]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
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.
which angle is congruent to
The angle congruent to ∠CGD is the angle ∠AGF as they are vertical angles.
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
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
is the expression 15y a coefficient or a constant
ASAP
Answer: The expression is not a coefficient, so it is a constant.
Step-by-step explanation:
Answer:
Constants are the terms in an expression that includes only numbers, the value of which does not change. Coefficient of a variable is the number written along with the variable in the term. So the expression 15y is a coefficient.
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
Over the course of 5 hours, the temperature dropped 10°C.
The temperature dropped the same number of degrees each hour.
What operation represents
the change in temperature
each hour?
Using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operations which represent this is 10/5 = 2°C.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."
The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, the operation that represents the change in temperature:
Time taken is 5 hours.
The temperature drop is 10°C.
The same amount of temperature in each hour.
Then, the operation will be:
10/5 = 2°C
Therefore, using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operation which represents this is 10/5 = 2°C.
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What is the solution to the system of equations graphed below?
Answer:
(0,-4)
Step-by-step explanation:
write the coordinates of the point where the two lines intercept themselves
Answer:
A. (0,-4)
x is 0 and y is -4
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
Choose all the sets containing the number pi
natural numbers
whole numbers
integers
rational numbers
irrational numbers
real numbers
Answer:
π is an irrational number, so it is also a real number.
A local produce stand has eight pumpkins on display the diameters of the pumpkin in inches are given in the table
SOLUTION
We will be pairing the pumpkins as follows
AB, CD, EF and GH
For AB, we have
[tex]\begin{gathered} 16\frac{1}{2}\div5\frac{1}{2} \\ \frac{33}{2}\div\frac{11}{2} \\ \frac{33}{2}\times\frac{2}{11} \\ =\frac{33}{11} \\ =3 \end{gathered}[/tex]Hence B is 3 times larger than A
For C and D, we have
[tex]\begin{gathered} 41\frac{1}{4}\div8\frac{1}{4} \\ \frac{165}{4}\div\frac{33}{4} \\ \frac{165}{4}\times\frac{4}{33} \\ =\frac{165}{33} \\ =5 \end{gathered}[/tex]Hence D is 5 times larger than C
E and F, we have
[tex]\begin{gathered} 13\frac{3}{4}\div3 \\ \frac{55}{4}\div\frac{3}{1} \\ \frac{55}{4}\times\frac{1}{3} \\ =\frac{55}{12} \\ =4.5833333333 \\ =4.583 \end{gathered}[/tex]Hence E is 4.583 times larger than F
And the last G and H, we have
[tex]\begin{gathered} 22\frac{3}{4}\div10\frac{1}{2} \\ \frac{91}{4}\div\frac{21}{2} \\ \frac{91}{4}\times\frac{2}{21} \\ =\frac{91}{21\times2} \\ =\frac{91}{42} \\ =2.167 \end{gathered}[/tex]Hence G is 2.167 times larger than H
The scale on the map shows that 4 cm = 52 miles. How many miles apart are two towns if the measurement is 22 cm?
The distane between two towns can be determined as,
[tex]\begin{gathered} 4\text{ cm=52 miles} \\ 1\text{ cm=}\frac{52\text{ miles}}{4} \\ =13\text{ miles} \\ 22\text{ cm=22}\times13\text{ miles} \\ =286\text{ miles} \end{gathered}[/tex]Thus, the required distance is 286 miles.
Factor completely, then place the factors in the proper location on the grid.
b2 - 7b + 12
Answer:
(b - 4)(b - 3)
Step-by-step explanation:
b² - 7b + 12
consider the factors of the constant term (+ 12) which sum to give the coefficient of the b- term (- 7)
the factors are - 4 and - 3 , since
- 4 × - 3 = + 12 and - 4 - 3 = - 7 , then
b² - 7b + 12 = (b - 4)(b - 3)
Shane bought 36 gallons of gas this week this amount is 6 gallons more than twice the amount of gas he bought last week how many gallons of gas in Shane by last week
so, she bought 15 gallons of gas last week
Explanation
Step 1
Let
36 gallons this week
x= number of gallons of gas Shane bought las week
this amount is 6 gallons more than twice the amount of gas he bought last week , then
[tex]36=2x+6[/tex]Step 2
solve for x
[tex]\begin{gathered} 36=2x+6 \\ \text{subtract 6 in both sides} \\ 36-6=2x+6-6 \\ 30=2x \\ \text{divide each side by 2} \\ \frac{30}{2}=\frac{2x}{2} \\ x=15 \end{gathered}[/tex]so, she bought 15 gallons of gas last week
I need the answer! I snap a pic to try n get it but no answer lol someone help!!! I’m on the clock
The given equation is
x^2 + 7x = 8
By subtracting 8 from both sides, it becomes
x^2 + 7x - 8 = 0
We would find two terms such that their sum or difference is 7x and the product is - 8x^2. The terms are - x and 8x. Replacing 7x with - x and 8x, we have
x^2 - x + 8x - 8 = 0
By factorising, we have
x(x - 1) + 8(x - 1) = 0
Since x - 1 is common, it becomes
(x + 8)(x - 1) = 0
x + 8 = 0 or x - 1 = 0
x = - 8 or x = 1
Option C is correct
A line has a slope of 2 and passes through the point (-2,8). What is the equation of theline?
The general equation of line passes through the point (x_1,y_1) and has slope m is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line passing through point (-2,8) and has slope of 2.
[tex]\begin{gathered} y-8=2(x-(-2)) \\ y=2\cdot x+2\cdot2+8 \\ y=2x+12 \end{gathered}[/tex]So answer is y = 2x + 12.
The total cost to develop camera pictures is proportional to the number of pictures being made. Maria paid 5.50 for 50 pics made. What number represents the constant in this proportional relationship.
Answer: 0.11
Step-by-step explanation:
Suppose y represents the cost, x represents the number of pictures, then y=kx {positive proportional function}
when x=50, y=5.5
5.5=50k
k=5.5/50
k=55/500
k=0.11
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
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.
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.
Which set of ordered pairs does not represent a function?
O {(6, 7), (-4,-5), (-1, 7), (-9, -7)}
O{(-6, 1), (-9, -6), (6, 7), (1, -8)}
O {(5,9), (7,2), (1,6), (-6,9)}
O {(-1, 1), (4, -6), (-3,0), (-3, 8)}
Answer:
it's 4
Step-by-step explanation:
#4 because we can see how x repeats its self 2 times such as (-3,0) and (-3,8)
What is the vertex of the graph of p(x) = x2 +6 ?
The graph p(x) = x² + 6 is a parabola. The equation can also be written as y = x² + 6.
A parabola follows the standard equation y = a (x - h)² + k where the vertex is (h,k).
From our equation y = x² + 6, we can convert this into a standard form which is y = 1 (x - 0)² + 6. Please take note that this standard form is just equal to the given equation.
From this converted standard form y = 1 (x - 0)² + 6, we can see that our h = 0, and our k = 6, therefore, our vertex is found at point (0,6).
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
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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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.
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