Answer:
Step-by-step explanation:
11/12 ÷ 1/3 = 2 3/4, or 11/2 as a improper fraction
hope this helps
Answer:
11/12 divided by 1/3 is the same as 11/12 * 3/1, which is 33/12.
Step-by-step explanation:
Which is the graph of f(x) = 2(3)x
Anna is making a sculpture in the shape of a triangular prism. The triangular bases have sides of 10m 10m and 12m and the height is 8m. She wants to coat it in a special finish so it preserves longer. if the sculpture is 5m thick what is the total area she will have to cover with the finish
12. A plot of land is used to grow flowers. of the land is allocated for orchids. 2 After the orchids have been planted, of the remaining land is allocated for roses. After orchids and roses have been planted, 0.75 of the remaining land is allocated for tulips. What fraction of the plot of land is not occupied by the flowers?
The fraction of the plot of land not occupied by the flowers is 0.0625 or 1/16.
Let's calculate the fraction of the plot of land that is not occupied by the flowers.
Given that initially, 1/4 of the land is allocated for orchids, we have 1 - 1/4 = 3/4 of the land remaining.
After planting the orchids, 2/3 of the remaining land is allocated for roses. Therefore, the fraction of land allocated for roses is (2/3) * (3/4) = 2/4 = 1/2.
Subtracting the land allocated for roses from the remaining land, we have 3/4 - 1/2 = 1/4 of the land remaining.
Finally, 0.75 of the remaining land is allocated for tulips. Therefore, the fraction of land allocated for tulips is 0.75 * (1/4) = 0.1875.
To find the fraction of the plot of land not occupied by the flowers, we subtract the fractions of land allocated for flowers from 1:
1 - (1/4 + 1/2 + 0.1875) = 1 - 0.9375 = 0.0625.
Therefore, the fraction of the plot of land not occupied by the flowers is 0.0625.
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Label each point on the number line with the correct value. Click each dot on the image to select an answer. Choices:
Answer:
- 4/2
Step-by-step explanation:
Answer:
A= 0.62 B= 7/9 C= 10/9
Step-by-step explanation:
Only one of the numbers is greater than 1, so 10/9 must belong on point C to the right of 1
We see that the other numbers appear near 2/3 on the number line Let's compare each with 2/3 to estimate their positions.
2/3 = 6/9
7/9 has the same denominator, but a larger numerator than 6/9 so 7/9 is further above 0 then 2/3 is. Even though 0 does not appear on the number line, it is left of any positive number. That means 7/9 is point B.
Lets convert 2/3 to a decimal to compare it with our decimal value.
2/3 = 0.6666
The numbers 0.62 and 0.6 have the same numbers of units and tenths. However, 0.6 has more hundredths, so it is farther above 0. So 0.62 is point A. (* ̄▽ ̄)b
Carlos plotted the points (-4,-4) and (0, 3) and connected them with a line, as shown below.
What is the slope between the two points?
Answer:
The slope between the two points is 7/4
Step-by-step explanation:
Slope of a Line
Suppose we know a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)
The points plotted by Carlos are (-4,-4) and (0,3), thus the slope is:
\(\displaystyle m=\frac{3-(-4)}{0-(-4)}\)
\(\displaystyle m=\frac{7}{4}\)
The slope between the two points is 7/4
Jaime had 15 meters of wire. He used 2/5 of this to his bedroom. How many meters of wire did he used?
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.
One possible set could be 3 cm, 4 cm, and 5 cm.
To verify if this set forms a right triangle, we can apply the Pythagorean theorem.
Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.
Adding these two values together gives us 25.
Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.
It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.
There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.
These sets are known as Pythagorean triples.
Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.
In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
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Which is more, 6 liters or 6,001 milliliters?
Answer: 6,001 milliliters
Step-by-step explanation: 6 Liter translates to 6,000 milliliters, which is 1 less than 6,001 milliliters.
Answer:
I believe 6 liters is more.
A 10 kg ball moves at a speed of 15m/s. The ball collides with a wall causing it to rebound in the opposite direction at a speed of 23 m/s.
Calculate the impulse on the ball?
Answer:
The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.
The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.
So, the impulse on the ball is -80 kg m/s.
How do I fine the slope of the line?
1 х Given g(x)=
\( \sqrt[3]{x} \)
and h(x) =
\( \frac{1}{ {x}^{3} } \)
(a) Find f(x) such that (fogoh)(x)=
\( \frac{x}{x + 1} \)
Determine the domain of (fogoh) (x)
(a) Since \(g(x)=\sqrt[3]{x}\) and \(h(x) = \frac1{x^3}\), we have
\((g\circ h)(x) = g(h(x)) = g\left(\dfrac1{x^3}\right) = \sqrt{3}{\dfrac1{x^3}} = \dfrac1x\)
We're given that
\((f \circ g \circ h)(x) = f(g(h(x))) = f\left(\dfrac1x\right) = \dfrac x{x+1}\)
but we can rewrite this as
\(\dfrac x{x+1} = \dfrac{\frac xx}{\frac xx + \frac1x} = \dfrac1{1+\frac1x}\)
(bear in mind that we can only do this so long as x ≠ 0) so it follows that
\(f\left(\dfrac1x\right) = \dfrac1{1+\frac1x} \implies \boxed{f(x) = \dfrac1{1+x}}\)
(b) On its own, we may be tempted to conclude that the domain of \((f\circ g\circ h)(x) = \frac1{1+x}\) is simply x ≠ -1. But we should be more careful. The domain of a composite depends on each of the component functions involved.
\(g(x) = \sqrt[3]{x}\) is defined for all x - no issue here.
\(h(x) = \frac1{x^3}\) is defined for all x ≠ 0. Then \((g\circ h)(x) = \frac1x\) also has a domain of x ≠ 0.
\(f(x) = \frac1{1+x}\) is defined for all x ≠ -1, but
\((f\circ g\circ h)(x)=f\left(\frac1x\right) = \dfrac1{1+\frac1x}\)
is undefined not only at x = -1, but also at x = 0. So the domain of \((f\circ g\circ h)(x)\) is
\(\left\{x\in\mathbb R \mid x\neq-1 \text{ and }x\neq0\right\}\)
use the figure to find x.
Answer:
\(20\sqrt{6}\)
Step-by-step explanation:
In all 30-60-90 triangles, the side lengths are in the ratio \(x:x\sqrt{3}:2x\), where \(2x\) is the hypotenuse and \(x\) is the side opposite to the 30 degree angle. Therefore, the hypotenuse of the 30-60-90 triangle (left) is \(2\cdot 10\sqrt{3}=20\sqrt{3}\). This hypotenuse also represents one leg of the 45-45-90 triangle.
In all 45-45-90 triangles, the side lengths are in ratio \(x:x:x\sqrt{2}\) where \(x\sqrt{2}\) is the hypotenuse of the triangle. Therefore, since \(x\) is the hypotenuse of the triangle marked and \(20\sqrt{3}\) is one of the legs, the value of \(x\) must be:
\(20\sqrt{3}\cdot \sqrt{2}=\boxed{20\sqrt{6}}\)
Answer:
\(x = 20\sqrt6\)
Step-by-step explanation:
The triangle with the side that has a measure of (\(10 \sqrt{3}\)) is a (30 - 60 - 90) triangle. This means that its angles are (30), (60), and (90) degrees. One property of a (30 - 60 -90) triangle is the ratio of its sides. This ratio, in simple terms, can be defined as the following:
angle : opposite side
\(30 : z\\60 : z\sqrt{3}\\90 : 2z\)
Use this property here to find the measure of the side opposite the (90) degree angle, that is shared between the two triangles.
This side is opposite the (30) degree angle, therefore, multiply this side by (2) will yield the measure of the side opposite the (90) degree angle. Therefore the side opposite the (90) degree angle has the following measure:
\(20\sqrt{3}\)
The triangle with a side of (x) is a (45 - 45 - 90) triangle. This means that its angles have a measure of (45 - 45 - 90). The ratios of the sides of a (45 - 45 - 90) triangle are as follows:
angle : opposite side
\(45:y\\45:y\\90:y\sqrt{2}\)
Apply this ratio here; multiply the side shared between the (30 - 60 - 90) triangle and (45 - 45- 90) triangle by (\(\sqrt{2}\)) in order to get the side with a measure of (x). When this is done, one gets the following result:
\(x = 20\sqrt{3}*\sqrt{2}\\x = 20\sqrt{6}\)
It is expected that 30% of the criminals in our prisons are violent offenders, 65% are nonviolent, and 5% are actually innocent. A sample of 300 inmates showed that 90 were violent offenders, 200 were nonviolent, and 10 were innocent. At the .05 significance level, can we conclude that the observed frequencies are different than the expected frequencies?
I need help with this problem from the calculus portion on my ACT prep guide
Given a series, the ratio test implies finding the following limit:
\(\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=r\)If r<1 then the series converges, if r>1 the series diverges and if r=1 the test is inconclusive and we can't assure if the series converges or diverges. So let's see the terms in this limit:
\(\begin{gathered} a_n=\frac{2^n}{n5^{n+1}} \\ a_{n+1}=\frac{2^{n+1}}{(n+1)5^{n+2}} \end{gathered}\)Then the limit is:
\(\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=\lim _{n\to\infty}\lvert\frac{n5^{n+1}}{2^n}\cdot\frac{2^{n+1}}{\mleft(n+1\mright)5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert\)We can simplify the expressions inside the absolute value:
\(\begin{gathered} \lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert \\ \lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert=\lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert \\ \lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert=\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert \end{gathered}\)Since none of the terms inside the absolute value can be negative we can write this with out it:
\(\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}\)Now let's re-writte n/(n+1):
\(\frac{n}{n+1}=\frac{n}{n\cdot(1+\frac{1}{n})}=\frac{1}{1+\frac{1}{n}}\)Then the limit we have to find is:
\(\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}\)Note that the limit of 1/n when n tends to infinite is 0 so we get:
\(\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}=\frac{2}{5}\cdot\frac{1}{1+0}=\frac{2}{5}=0.4\)So from the test ratio r=0.4 and the series converges. Then the answer is the second option.
Ms. Jaffey had a total of 428.5 ounces of pretzels to put into 5 bowls for a party. She put an equal number of ounces of pretzels into each bowl. How many ounces of pretzels did Ms. Jaffey put into each bowl?
Ms. Jaffey put approximately 85.7 ounces of pretzels into each bowl.
To find out how many ounces of pretzels Ms. Jaffey put into each bowl, we need to divide the total number of ounces by the number of bowls.
Ms. Jaffey had a total of 428.5 ounces of pretzels, and she distributed them equally among 5 bowls. Therefore, we can divide the total number of ounces by 5 to determine the amount in each bowl.
428.5 ounces ÷ 5 bowls = 85.7 ounces.
So, Ms. Jaffey put approximately 85.7 ounces of pretzels into each bowl.
Since it's unlikely to have exact measurements when dividing a total quantity into equal parts, we round the result to one decimal place, giving us 85.7 ounces. This means that each bowl contains approximately 85.7 ounces of pretzels.
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After plotting the data where x=the side of a polygon, and f(x) = the area of the polygon, Jack used technology and
determined the appropriate model to approximate the area of the polygon, F(x) = x^2 + 3x + 2. Use the model Jack
created to predict the area of a polygon that has a side length of 3.
10
18
19
020
Answer: 19
Step-by-step explanation:
As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1
Therefore, f(3) = 19
Sibusiso's car consumes petrol at a rate of 7,6 l/100km. The petrol tank in his car holds 65litres. How far can he ride on a full tank of petrol, rounded off to the nearest kilometre?
Answer:
6 +67 _^76 + 9 x 2087 - 9012 = 1000
Step-by-step explanation:
98 + 2000 - 76 = 1000
7.52 divided by 64 =
What is the domain of the square root function graphed below?
using the the letters JOYFUL how many two-letter combinations can be found
Answer:
foul,and flu.
Step-by-step explanation:
I was doing math then I got this question wrong.
Why is C not on the y-axis, and why is b on y-axis.
The options that correctly show the points of the given graph are;
Option 4: A is on the y-axis
Option 5; D is on the x-axis
How to interpret the axis of a graph?Usually in mathematical equation graphs, the y-axis represents the range of the function which is a set of all possible output values for given input values . Whereas, the domain is usually represented on the x-axis and it shows the set of all possible input values of the function.
Now, from the given graph, we see the following;
A is on the y-axis
B is at the origin
C is at the point (1, 2)
D is on the x-axis
Looking at the options, we can tell that options 4 and 5 are correct representations of the given graph because they correctly denote the points on the x-axis and y-axis.
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Which of the following is the most significant greenhouse gas due to its long lifespan in the environment?
A. Carbon dioxide
B. Argon dioxide
C. Oxygen
D. Nitrogen Oxide
Answer:
Carbon dioxide
Step-by-step explanation:
I think it’s carbon dioxide because, it is the most significant greenhouse gas. I also think it’s the carbon dioxide because the question is asking which one it is and I chose carbon dioxide.
please help me asap
Answer: Number 1: = and Number 2: is C
Step-by-step explanation:
Answer:
6. >
7. 5/6, 2/3, 8/15
Step-by-step explanation:
For 6, you need to make the denominators equal, so you need to multiply 6/3*5 making it 30/15. Now which is greater 30/15 or 10/15 and you can see it's 30/15 so it would be >. For 7 you need to do the same thing but make all three denominators the same. 2/3 becomes 20/30 by multiplying by 10. 5/6 becomes 25/30 by multiplying by 5. Lastly, 8/15 becomes 16/30 by multiplying by 2. Now all their denominators are the same, so now all you have to do is order them. 25/30, 20/30, and 16/30. This is equal to 5/6, 2/3, 8/15.
What is 2 times 2 equal to
You have the exercise "2 times 2". The word "times" indicates that it is a Multiplication. Then, you can rewrite this operation in the following form:
\(2\cdot2\)That Multiplication indicates that you need to add 2 two times, as follows:
\(2+2\)Therefore, based on the explained, you can determine that:
\(2\cdot2=2+2=4\)Hence, the answer is:
\(4\)true or false
1. the normal curve concept applies to a large sample pf scores.
2. an interval estimate depends on a confidence level
the answer of question 1 is true
the answer of question 2 is true
A marble is selected from a bag containing eight marbles numbered 1 to 8. The number of the marble selected will be recorded as the outcome. Consider the following events. Event A: The marble selected has an even number.
Event B: The marble selected has a number from 3 to 6.
a) Event "A or B":
b) Event "A and B":
c) The complement of the event A.
A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
Step-by-step explanation:MAKE A PLAN:
List The OUTCOMES for EACH EVENT and their COMBINATIONS:
SOLVE THE PROBLEM:a) - EVENT "A": {2, 4, 6, 8}
EVENT "B": {3, 4, 5, 6}
EVENT "A" or "B": {2, 3, 4, 5, 6, 8}
b) - EVENT "A" or "B": {4, 6}
c) - The COMPLEMENT of the EVENT "A": {1, 3, 5, 7}
Draw the conclusion:A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
I hope this helps!
Sabas Company has 40,000 shares of $100 par, 1% preferred stock and 100,000 shares of $50 par common stock issued and outstanding. The following amounts were distributed as dividends: Year 1: $50,000 Year 2: 90,000 Year 3: 130,000 Determine the dividends per share for preferred and common stock for each year. If an answer is zero, enter '0'. Round all answers to two decimal places.
The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.
To determine the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.
Preferred Stock:
Dividends per share of preferred stock = Total dividends for preferred stock / Number of preferred shares
Year 1:
Dividends per share of preferred stock for Year 1 = $50,000 / 40,000 shares = $1.25
Year 2:
Dividends per share of preferred stock for Year 2 = $90,000 / 40,000 shares = $2.25
Year 3:
Dividends per share of preferred stock for Year 3 = $130,000 / 40,000 shares = $3.25
Common Stock:
Dividends per share of common stock = Total dividends for common stock / Number of common shares
Year 1:
Dividends per share of common stock for Year 1 = ($50,000 - Total dividends for preferred stock) / 100,000 shares = ($50,000 - $50,000) / 100,000 shares = $0
Year 2:
Dividends per share of common stock for Year 2 = ($90,000 - Total dividends for preferred stock) / 100,000 shares = ($90,000 - $90,000) / 100,000 shares = $0
Year 3:
Dividends per share of common stock for Year 3 = ($130,000 - Total dividends for preferred stock) / 100,000 shares = ($130,000 - $130,000) / 100,000 shares = $0
The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.
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Please help asap !!! I will give points !!!
The value of p when q is 2 is 1
What is inverse variation?Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
This means that has x increases y will decrease and vice versa.
If p is inversely proportional to q , then p = kq
when p = 2, q = 4
2 = k4
k = 2/4
k = 1/2
When q = 2
p = 1/2 × 2
p = 1
Therefore the value of p is 1
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PLEASE HELP
i need my algebra 2 credit !!!
Police estimate that 20% of drivers do not wear their seatbelts. The police set up a safety roadblock and stopping cars to check for seatbelt use. If the police team stops 30 cars during the first hour, what is the standard deviation?
If Police estimate that 20% of drivers do not wear their seatbelts. The police set up a safety roadblock and stopping cars to check for seatbelt use. If the police team stops 30 cars during the first hour, the standard deviation is 2.191.
How to find the standard deviation?Using this formula to find the Standard deviation
Standard deviation = √ Sample size × Estimated drivers × (1 - Estimated drivers)
Let plug in the formula
Standard deviation = √ 30 × 0.20 × (1- 0.20)
Standard deviation = √ 30 × 0.20 × 0.80
Standard deviation = √ 4.8
Standard deviation = 2.191
Therefore we can conclude that the standard deviation is 2.191.
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