Answer:
$9.
Step-by-step explanation:
We have been given that Shen’s mother gave him $10 to go buy groceries. He picked up a gallon of milk for $3.49, three pounds of oranges that cost $1.14 per pound, and a box of cereal for $3.46.
In front-end estimation, we round whatever number is in front instead of rounding each number to a given place value.
We can see that in $3.49, front number is and second number is less than 5, so we will round it down to $3.
Similarly, in $3.46, 1st number is 3 and second number is less than 5, so we will round it down to $3.
In $1.14, front or 1st number is 1 and second number is less than 5, so we will round down to $1. Cost of three orange boxes would be [tex]\$1*3=\$3[/tex].
[tex]\text{Total estimated cost}=\$3+\$3+\$3[/tex]
[tex]\text{Total estimated cost}=\$9[/tex]
Therefore, the total estimated cost of groceries is $9.
The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2)=
Answer:
The correct answer is f(-2)= -2
Step-by-step explanation:
It takes an older pump twice as long to drain a certain pool as it does a newer pump. working together, it takes the two pumps 3 hours to drain the pool. how long will it take the newer pump to drain the pool working alone
It would take the newer pump 4.5 hours to drain the pool working alone.
Given that,
It takes an older pump twice as long to drain a certain pool as it does a newer pump.
Let us assume that,
The time it takes for the newer pump to drain the pool alone is x hours.
Hence, According to the information given, the older pump takes twice as long, so it would take 2x hour to drain the pool alone.
Now, When both pumps work together, their combined rate of draining the pool is additive.
Therefore, the equation is,
[tex]\dfrac{1}{x} + \dfrac{1}{2x} = \dfrac{1}{3}[/tex]
Simplify the equation for x,
[tex]\dfrac{(2 + 1)}{2x} = \dfrac{1}{3}[/tex]
[tex]\dfrac{(3)}{2x} = \dfrac{1}{3}[/tex]
Cross multiplication,
[tex]3 \times 3 = 2x[/tex]
[tex]2x = 9[/tex]
Dividing both sides by 2:
[tex]x = 4.5[/tex]
Therefore, it would take the newer pump 4.5 hours to drain the pool working alone.
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What is the slope of the line passing through the points (−3, 4) and (4, −1)?
35
−1
−57
3
Answer:
the answer is C. -5/7
There are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour. how many minutes are in a month?
It is found that there are 43,800 minutes in a month.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We knowt that there are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour.
1 day = 24 hour
1 hour = 60 minutes.
1 minutes = 60 seconds
Therefore, 24 hours = 24 x 60 = 1440 minutes
There are 1440 minutes in one day.
Then 30 days = 30 x 1440 = 43,800
Hence, It is found that there are 43,800 minutes in a month.
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Which set of ordered pairs could be generated by an exponential function?
Use the graph below to answer the following question:
What is the average rate of change from x = –4 to x = 1?
A. -3
B. -1
C. 0
D. 1
Two step equations
6=a/4+2
a =16 is the solution of the given equation.
To solve the equation 6 = a/4 + 2, we'll perform two steps to isolate the variable 'a'.
Step 1: Subtract 2 from both sides of the equation:
6 - 2 = a/4 + 2 - 2
4 = a/4
Step 2: Multiply both sides of the equation by 4 to get rid of the fraction:
4 * 4 = (a/4) * 4
16 = a
Therefore, the solution to the equation is a = 16.
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The product of three numbers is -216 but their sum is -18. What are these three numbers?
A nervous kicker usually makes 70% of his first field goal attempts. if he makes his first attempt, his success rate rises to 90%. what is the probability that he makes his first two kicks?
The probability that the kicker makes his first two kicks is 0.63, or 63%.
Let's denote the events:
A: The kicker makes his first kick
B: The kicker makes his second kick
Given:
P(A) = 0.7 (probability that the kicker makes his first kick)
P(B|A) = 0.9 (probability that the kicker makes his second kick given that he made his first kick)
To find the probability of both events A and B occurring (the kicker making his first two kicks), we can use the multiplication rule of probability:
P(A and B) = P(A) * P(B|A)
Substituting the given probabilities, we have:
P(A and B) = 0.7 * 0.9 = 0.63
Therefore, the probability that the kicker makes his first two kicks is 0.63, or 63%.
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The probability that the kicker makes his first two kicks is 0.63, or 63%.
Explanation:To find the probability that the kicker makes his first two kicks, we need to multiply the probabilities of each individual kick.
The kicker has a 70% chance of making his first kick, which means he has a 30% chance of missing it.
If the first kick is made, his success rate rises to 90%. So, the probability of making the second kick, given that he made the first kick, is 90%.
To find the probability of both kicks being made, we multiply the probability of making the first kick (0.7) with the probability of making the second kick given that the first kick was made (0.9).
0.7 * 0.9 = 0.63
Therefore, the probability that the kicker makes his first two kicks is 0.63, or 63%.
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Find m∠abc
Geometry>Proving Angles Congruent
the measure of angle ABC (m∠ABC) is 130 degrees. it's essential to recognize that the sum of the angles along a straight line is always 180 degrees.
In this case, we have two angles, 2x and 5x+5, forming a straight line with an unknown angle (m∠ABC). So, we set up the equation:
2x + 5x + 5 = 180
Next, combine the like terms on the left side:
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25
Therefore, the measure of angle ABC = 5x + 5
= 5(25) + 5
=130 degree
So, the measure of angle ABC (m∠ABC) is 130 degrees.
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Determine the intercepts of the line. y=-7x+3y=−7x+3
Answer:
Step-by-step explanation:
y=−7x+3x intercept when y = 0so-7x + 3 = 0-7x = -3 x = 3/7y intercept when x = 0 so y = 3
answer
x intercept (3/7 , 0)y intercept (0, 3)
True or false in a two column proof the right column states your reasons
In two column proof the right column states your reasons is true statement.
In a two-column proof, the right column typically contains the statements of reasons or justifications for each step taken in the left column.
The left column contains a sequence of statements that represent the logical progression of the proof, while the right column provides the reasoning or logical basis for each step to show that it follows from the previous statements.
This format is commonly used in geometry to provide a clear and organized presentation of the proof's logical structure.
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Write the following inequality in slope-intercept form. −6x + 2y ≤ 42
Answer: The required slope-intercept form is [tex]y\leq 3x+21.[/tex].
Step-by-step explanation: We are given to write the following inequality in slope-intercept form :
[tex]-6x+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the slope-intercept form of an inequality of the given form is as follows :
[tex]y\leq mx+c,[/tex] where m is the slope and c is the y-intercept.
From inequality (i), we have
[tex]-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq\dfrac{6}{2}x+\dfrac{42}{2}\\\\\Rightarrow y\leq 3x+21.[/tex]
Thus, the required slope-intercept form is [tex]y\leq 3x+21.[/tex].
The length and the width of a rectangle are both doubled. What is the ratio of the area of the larger rectangle to the area of the smaller rectangle?
I think it is 2:1. Am I right? If not, what is the ratio?
What is the least angle measure by which this figure can be rotated so that it maps onto itself? 45° 90° 180° 360° Left right double headed arrow.
In mathematics, specifically geometry, the least angle measure by which a regular, symmetric figure can be rotated to map onto itself is usually 90°. This concept falls under the umbrella of rotational symmetry.
Explanation:The question is about rotation of objects in geometry. To identify the least angle measure for a figure to map onto itself, we need to know the shape of the figure. However, assuming the figure is regular and symmetric (a square or a rectangle for example), the least angle measure by which it can be rotated to map onto itself is 90°.
It's important to remember the concept of rotational symmetry. A figure has rotational symmetry if it can be rotated less than 360° around a central point and still appear the same. For instance, a regular rectangle or square has a rotational symmetry of 90°, since we can rotate it 90 degrees and it appears the same.
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You need five liters of yoda soda for every 12 guests if you have 36 guests how many liters do you need
What is the factored form of 5x2 + 28x + 15?
Let f(x)=−3x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
What is the equation for g(x) ?
Enter your answer in the box.
g(x)= ___________
The graph of the function f(x)=|3x| is translated 4 units up.
What is the equation of the transformed function?
Enter your answer in the box.
g(x)= ___________
Ques 1)
[tex]g(x)=-12x+48[/tex]
Ques 2)
[tex]g(x)=|3x|+4[/tex]
Step-by-step explanation:Ques 1)
We know that if a graph is stretched by a factor of a then the transformation if given by:
f(x) → a f(x)
Also, we know that the translation of a function k units to the right or to the left is given by:
f(x) → f(x+k)
where if k>0 then the shift is k units to the left
and if k<0 then the shift is k units to the right.
Here the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
This means that the function g(x) is given by:
[tex]g(x)=4f(x-4)\\\\i.e.\\\\g(x)=4(-3(x-4))\\\\i.e.\\\\g(x)=-12(x-4)\\\\i.e.\\\\g(x)=-12x+48[/tex]
Ques 2)
We know that the transformation of the type:
f(x) → f(x)+k
is a shift or translation of the function k units up or down depending on k.
If k>0 then the shift is k units up.
and if k<0 then the shift is k units down.
Here, The graph of the function f(x)=|3x| is translated 4 units up.
This means that the transformed function g(x) is given by:
[tex]g(x)=|3x|+4[/tex]
Answer:
-12(x-4)
Step-by-step explanation:
I just took the test this is the answer!! Basically you take -3 and 4 and times it which would be -12. You then have x and another 4 left over. Since you are translating to the right you will be negative therefore giving us the answer -12(x-4).
Translate the following statement to an inequality.
A number is at most seven.
x > 7
x < 7
x ≥ 7
x ≤ 7
Answer:
x ≤ 7
Yuuupeeee
How did the great pyramid of giza get 30 feet shorter?
PLEASE HELP!!!!Which equation shows y=3/4x−5/2 in standard form?
A) 3x−4y=10
B)4x−3y=10
C)4x−3y=−10
D)3x−4y=−10
2.What is the slope-intercept form of the linear equation x + 4y = 12? Enter your answer in the box.
3.Graph the equation on the coordinate plane. y=1/2x
Answer: 1. A) 3x−4y=10
2. [tex]y=-\frac{x}{4}+3[/tex]
3. In the attachment.
Explanation:
1. Given equation=[tex]y=\frac{3}{4}x-\frac{5}{2}[/tex]
To reduce it into standard form , multiply both sides by 4,we get
[tex]4y=4(\frac{3}{4}x-\frac{5}{2})\\\Rightarrow4y=3x-10......[distributive\ property]\\\Rightarrow3x-4y=10[/tex] which is option A.
2. Given linear equation : x+4y=12
The standard slope intercept form is given by y=mx+c where m is the slope and c is the constant.
To reduce given linear equation subtract x from both sides, we get
4y=12-x
Divide 4 on both sides.
[tex]\Rightarrow\ y=\frac{12-x}{4}=3-\frac{x}{4}\\\Rightarrow\ y=-\frac{x}{4}+3[/tex] is the slope-intercept form of the linear equation x + 4y = 12.
3. To graph equation [tex]y=\frac{1}{2}x[/tex] on the coordinate plane.
We need to find points to plot the line
Put x=0,we get y=0
Put x=2,we get y=1
Thus we have points (0,0) and (2,1) to plot the line on the graph.
Answer: 1. A) 3x−4y=10
Step-by-step explanation:
At a canning company the daily production cost, y, is given by the quadratic equation y = 650 – 15x + 0.45x2, where x is the number of canned items. What is the MINIMUM daily production cost?
A) $1,025.00 B) $1,186.25 C) $525.00 D) $536.25
Answer:
Option C) is correct
Step-by-step explanation:
Given : y is the daily production cost at a canning company such that [tex]y=650-15x+0.45x^2[/tex] wherex is the number of canned items .
To find : Minimum daily production cost
Solution :
[tex]y=650-15x+0.45x^2[/tex]
On differentiating both sides with respect to x, we get
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=-15+0.9x[/tex]
On putting [tex]\frac{\mathrm{d} y}{\mathrm{d} x}=0[/tex] , we get [tex]-15+0.9x=0\Rightarrow 15=0.9x\Rightarrow x=\frac{15}{0.9}=\frac{150}{9}=\frac{50}{3}[/tex]
We get intervals as \left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty \right )[tex]\left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty \right )[/tex]
For [tex]x=0\epsilon \left ( -\infty ,\frac{50}{3} \right )[/tex] , [tex]f'(0)=-15< 0[/tex]
For [tex]x=16\epsilon \left ( \frac{50}{3},\infty \right )[/tex] , [tex]f'(18)=-15+0.9(18)=-15+16.2=1.2> 0[/tex]
Therefore, [tex]y=\frac{50}{3}[/tex] is a point of minima.
So, minimum cost is equal to [tex]y\left ( \frac{50}{3} \right )[/tex]
[tex]y\left ( \frac{50}{3} \right )=650-15\left ( \frac{50}{3} \right )+0.45\left ( \frac{50}{3} \right )^2=650-250+125=\$ 525[/tex]
So, option C) is correct .
The composition is applied to △RST to create the image of △R"S"T", which is not shown.
What are the coordinates of point S"?
Answer:
S''(-3/2, 9/2)
Step-by-step explanation:
In a dilation, the coordinates of every ordered pair in the pre-image are multiplied by the scale factor to create the ordered pairs of the image.
The first dilation has a scale factor of 1/2. This maps:
R(-6, 10)→R'(-6/2, 10/2) = R'(-3, 5)
S(-2, 6)→S'(-2/2, 6/2) = S'(-1, 3)
T(-10, 0)→T'(-10/2, 0/2) = T'(-5, 0)
The second dilation has a scale factor of 3/2:
R'(-3, 5)→R''(-9/2, 15/2)
S'(-1, 3)→S''(-3/2, 9/2)
T'(-5, 0)→T''(-15/2, 0)
This makes S'' have coordinates (-3/2, 9/2).
Answer: a :)
Step-by-step explanation:
A population of bacteria doubles every 12 hours initially the population of bacteria is 80 what is the population of bacteria after 30 hours, rounded to the nearest whole number?
Answer:
not 480, answer is 453 according to K12.
Step-by-step explanation:
took the k12 test, the answer is in fact, 453.
The population of the bacteria after 30 hours will be 400.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the population of bacteria doubles every 12 hours initially the population of bacteria is 80 what is the population of bacteria after 30 hours?
The population will be calculated as,
12 hours = 2 times of 80
1 hour = 2 / 12 times of 80
30 hours = ( 30 x 2 x 80 ) / 12
30 hours = 400 bacterias
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−t/4=−3π
What is the answer to T
the value of (t) that satisfies the equation is approximately (37.6992).
Let's solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\).[/tex]
Step 1: Multiply both sides by \(-4\) to isolate \(t\).
[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4)\][/tex]
This simplifies to:
[tex]\[ t = 12\pi \][/tex]
Step 2: Substitute the value of \(\pi\) to get the final answer.
[tex]\[ t = 12 \times 3.14159 \][/tex]
[tex]\[ t = 37.6992 \][/tex]
Therefore, the value of ( t ) is approximately ( 37.6992 ).
To solve the equation [tex]\(-\frac{t}{4} = -3\pi\) for \(t\)[/tex] , we first want to isolate (t) on one side of the equation. To do this, we can multiply both sides of the equation by (-4). This cancels out the fraction and leaves us with (t) on the left side:
[tex]\[-\frac{t}{4} \times (-4) = -3\pi \times (-4) \\t = 12\pi\][/tex]
Now, to get the numerical value of \(t\), we substitute the value of \(\pi\), which is approximately \(3.14159\), into the equation:
[tex]\[ t = 12 \times 3.14159 \][/tex]
[tex]\[ t \approx 37.6992 \][/tex]
Therefore, the value of (t) that satisfies the equation is approximately (37.6992).
complete question
−t/4=−3π
What is the answer to T
Find the ratio of 1 feet. 4 inches. to 1 yard
The ratio of 1 foot 4 inches to 1 yard is 16:36 or 4:9.
To find the ratio of 1 foot 4 inches to 1 yard, we first need to convert both measurements to the same unit. Since there are 3 feet in a yard and 12 inches in a foot, we can express both measurements in inches.
1 foot is equivalent to 12 inches.
Therefore, 1 foot 4 inches is:
1 [tex]\times[/tex] 12 + 4 = 12 + 4 = 16 inches
Now, since there are 3 feet in a yard, and each foot has 12 inches, 1 yard is equivalent to:
3 [tex]\times[/tex] 12 = 36 inches
Now we have both measurements in inches, and we can set up the ratio:
16 inches: 36 inches
Therefore, the simplified ratio is:
16:36.
We can further simplify this ratio by dividing both numbers by 4:
(16/4):(36/4) = 4:9.
x = {(2, 4), (3, 4), (4, 4), (5, 4)} Is x a function and why?
Help me please! |-.-| The struggle is real...
2x^2-13x+4=0
solve using the quadratic formula
Charlie drove 864 miles in 12 hours. at the same rate, how long would it take him to drive 504 miles?
A coin is tossed 10 times:
How many times do you expect to get heads?
How many times do you expect to get tails?
Final answer:
The expected number of heads and tails when tossing a coin 10 times is 5 each.
Explanation:
If you toss a coin ten times:
Expected number of heads: 5
Expected number of tails: 5
This is because for each toss, the probability of getting a head is 0.5 (50%) and the same for a tail. Over multiple tosses, the outcomes tend to approach these expected values.