60.0 is the area of the triangle
Ebit goes from $30m to $33m; depreciation goes from $10m to $12m; and interest expense goes from $6 m to $8m. what is the percent change in the numerator of the cash coverage ratio? what is the percent change in the denominator of the cash coverage ratio?
i am pretty sure you add up all of them
The percent change in the numerator for the cash coverage ratio, considering the changes in EBIT and depreciation, is 12.5%. Meanwhile, the percent change in the denominator, based on the interest expense, is 33.33%.
Explanation:The cash coverage ratio is a measure of a company's ability to pay off its obligations and is calculated by adding depreciation and EBIT and then dividing by the interest expense. For this question, we are looking at the percent change in the numerator, which is EBIT + depreciation, and the denominator, which is the interest expense. With EBIT going from $30m to $33m, depreciation going from $10m to $12m, and interest expense going from $6m to $8m we can calculate as follows.
The original numerator value was $40m (EBIT of $30m + depreciation of $10m) and the new numerator is $45m (EBIT of $33m + depreciation of $12m). So, the percent change in the numerator of the cash coverage ratio is ((45-40)/40)*100 = 12.5%. The original denominator was $6m and the new denominator is $8m. Thus, the percent change in the denominator of the cash coverage ratio is ((8-6)/6)*100 = 33.33%.
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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The number of unshelled peanuts in a 1 lb container is normally distributed with a mean of 375 peanuts and a standard deviation of 24 peanuts.
Suppose 4000 different 1 lb containers are in a warehouse.
About how many containers contain more than 447 peanuts?
Answer: a) 6
Step-by-step explanation:
The mean is 375 which has a z-score of 0.
The standard deviation is 24 so:
z-score of 1 is: 375 + 24 = 399z-score of 2 is: 399 + 24 = 423z-score of 3 is: 423 + 24 = 477A z-score of 3 is 99.85% from the left (or 1 - 99.85% from the right = 0.15%)
Since we are looking for the "more than" a z-score of 3, it is 0.15% of the total.
4000
× 0.0015
6.0000
Can someone please check this? Thanks!
Answer:
Your choice is correct.
Step-by-step explanation:
The amplitude (multiplier of sin( )) is half the diameter, so is 17.5. The midline (value added to the sine function) is the difference between the maximum (50) and the amplitude (17.5), so is 50-17.5 = 32.5. All choices have the correct frequency.
The function will look like ...
f(t) = 17.5·sin(2πt/5) +32.5 . . . . . as you have marked
Which is never a chord?
I diameter
II radius
III secant
IV tangent
The distance between the center to the circumcenter is called a radius. The radius can not be a chord.
What is a chord of a circle?It is the distance between the two points in a circle that is known as a chord.
1 Diameter - If the chord length is longest then it is called the diameter. This can be a chord.
2 Radius - The distance between the center to the circumcenter is called a radius. This can not be a chord.
3 Secant - The line passing through the circle is known as a secant. This can be a chord.
4 Tangent - The line which touches the circle then line is called a tangent. This can be a chord.
More about the chord of a circle link is given below.
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Find the domain and range of f(x)=-2x+|3sinx|
Answer:
Domain: (-∞, ∞); range: (-∞, ∞).
Step-by-step explanation:
In the given function, f(x)= -2x + |3sinx|, the range of the |3sinx| term is [0, 3]. That of the -2x term is (-∞, ∞).
The range of f(x)= -2x+|3sinx| is thus (-∞, ∞); the |3sinx| term has no effect on this.
There are no restrictions on the input to f(x)= -2x+|3sinx|. The domain is thus (-∞, ∞).
The number of defective units in a production run of 850 circuit boards are normally distributed with 21 defective units and 3 defective units. Find the probability P(17 < X < 25) with the help of the graphing calculator. Round your answer to the nearest integer.
77%
81%
80%
82%
Answer:
82%
Step-by-step explanation:
We let the random variable X denote the number of defective units in the production run. Therefore, X is normally distributed with a mean of 21 defective units and a standard deviation of 3 defective units.
We are required to find the probability, P(17 < X < 25), that the number of defective units in the production run is between 17 and 25.
This can be carried out easily in stat-crunch;
In stat crunch, click Stat then Calculators and select Normal
In the pop-up window that appears click Between
Input the value of the mean as 21 and that of the standard deviation as 3
Then input the values 17 and 25
click compute
Stat-Crunch returns a probability of approximately 82%
Find the attachment below.
What percentage of the data values represented on a box plot falls between the minimum value and the lower quartile?
Answer:
first 25%
Step-by-step explanation:
A quartile is a quarter, so the first 25% falls between the minimum and lower quartile
Answer:
A. 25%
Step-by-step explanation:
Because it asks you where one section to another section (on a box plot there are four areas containing 25% within each one.)
scientists are studying the temperature on a distant planet. they find that the surface temperature at one location is 45 Celsius. they also find that the temperature decreases by 7 Celsius for each kilometer you go up from the surface.
let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). write an equation relating T to H, and then graph your equation using the axes.
Final Answer:
The equation[tex]\(T = 45 - 7H\)[/tex] represents the relationship between temperature (T) and height above the surface (H) on the distant planet, where the surface temperature is 45 Celsius, decreasing by 7 Celsius for each kilometer of height. Graphing this equation reveals a linear line with a negative slope, portraying the systematic decrease in temperature as one moves higher above the planet's surface.
Explanation:
The equation [tex]\(T = 45 - 7H\)[/tex] is derived from the given information about the distant planet's temperature. The surface temperature is 45 Celsius, and for each kilometer above the surface (represented by H), the temperature decreases by 7 Celsius.
The equation reflects this linear relationship. The term 45 is the starting temperature at the surface, and the term -7H represents the decrease for each kilometer above.
For example, let's substitute H = 1 into the equation to find the temperature at a height of 1 kilometer:
[tex]\[ T = 45 - 7(1) = 45 - 7 = 38 \][/tex]
This calculation shows that at a height of 1 kilometer, the temperature is 38 Celsius. Similarly, for H = 2:
[tex]\[ T = 45 - 7(2) = 45 - 14 = 31 \][/tex]
This process can be repeated for different values of H to create a set of coordinates (H, T) that form a linear relationship. Graphing these points produces a straight line with a negative slope, illustrating the temperature decrease with increasing height.
In essence, the detailed calculation demonstrates how the equation captures the specified temperature-height relationship on the distant planet. It provides a mathematical representation of the observed data and allows scientists to predict temperatures at various heights above the surface.
Lionel needs money quite frequently and doesn't need much interest at all. Which of these options for saving money is best for him?
A. savings bond
B. money market account
C. certificate of deposit
D. savings account
Answer: Savings account - Apex
Answer:
Option D is the correct answer.
Step-by-step explanation:
The saving bonds are a good way to earn money but they work at fixed rate of interest over a set time period.
Money market accounts give a limited access to account and not more than three checks are written in a month. Its a type of short term savings.
The certificate of deposit or CD's have higher interest rate than savings account. But one cannot withdraw the money before the term maturity otherwise penalty is to be paid.
Savings account are deposit accounts that can be accessed whenever needed. These yield less interest as compared to money market accounts or CD's.
Therefore, the best option for Lionel to choose will be Savings account
If triangle ABC is defined by the coordinates A(-4, -4), B(2, -2), C(0, 4) is dilated by a scale factor of 1 2 , with resulting vertex A' at (-2, -2). What is the center of the dilation?
Answer:
the origin, (0, 0)
Step-by-step explanation:
The coordinates of A' are 1/2 those of A, meaning each has been multiplied by the scale factor 1/2. When the dilated points are all the original points multiplied by the scale factor, the center of dilation is the origin.
_____
For center of dilation Q, the image of a point A after dilation by a factor of k is ...
A' = kA + (k-1)Q
Then for points A, A', and dilation factor k, the center of dilation can be found to be ...
(A' -kA)/(k-1) = Q
Here, that is ...
Q = ((-2, -2) -(1/2)(-4, -4))/(1/2 -1) = (0, 0)/(-1/2)
Q = (0, 0)
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The results of a poll show that the percent of people who want a new restaurant is in the interval (24%, 38%) . There are 112,483 people in the city.
What is the interval for the number of people who are likely to want this restaurant in their city?
Round to the nearest person.
Answer: (26996, 42744)
Step-by-step explanation:
24% of 112,483 = 26,995.92 --> rounded to the nearest person is 26,996
38% of 112,483 = 42,743.54 --> rounded to the nearest person is 42,744
The number of people who want a new restaurant is somewhere between 26,996 and 42,744.
Answer:
26,996-42,744
Step-by-step explanation:
To calculate the spam of the people that who are likely to want this restaurant you just have to multiply the total number people in the city by the two points in the extremes of the intervals.
24% * 112,483=26996
and the other one would be:
38%* 112,483= 42744
And those are the extremes of the interval of people in the city who are likely to want this new restaurant.
If you park 3 levels below the lobby floor of a hotel and take the elevator to the 15th floor, how many floors apart are you from your vehicle? Floors
I think 18 because 3+15=18
Answer:
I think it's 12
Step-by-step explanation:
15-3=12
Traci bought 1 1/4 yards of yellow ribbon, 2 5/6 yards of pink ribbon, and 3 1/2 yards of purple ribbon. How many did she buy altogether
The total ribbon is 7 whole 7/12 yards if the Traci bought 1 1/4 yards of yellow ribbon, 2 5/6 yards of pink ribbon, and 3 1/2 yards of purple ribbon.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Traci bought 1 1/4 yards of yellow ribbon, 2 5/6 yards of pink ribbon, and 3 1/2 yards of purple ribbon.
The total ribbon:
[tex]= \rm 1\dfrac{1}{4} +2\dfrac{5}{6} +3\dfrac{1}{2} \\\\=\rm \dfrac{5}{4}+\dfrac{17}{6}+\dfrac{7}{2}\\\\=\dfrac{15+34+42}{12}\\=\dfrac{91}{12}\\\\=7\dfrac{7}{12} \ yards[/tex]
Thus, the total ribbon is 7 whole 7/12 yards if the Traci bought 1 1/4 yards of yellow ribbon, 2 5/6 yards of pink ribbon, and 3 1/2 yards of purple ribbon
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Rico's backpack weighed 3.6 pounds. Then he added his school books which weighed an additional 24.76 pounds. How much did Rico's backpack weigh with his school books?
Answer:
The answer should be 28.36
Step-by-step explanation:
You add them together
Hope this helps!
Answer:
28.36
Step-by-step explanation:
3.6 + 24.7 = 28.36
please help me out with this one
answer choices :
- 3648
- 2632
- 1387
- 2109
Answer:
[tex]V = 2622\ in ^ 3[/tex]
Step-by-step explanation:
We have a composite figure, therefore the volume of the figure will be the sum of the volume of both figures.
The volume of the rectangular prism is the product of its length by its width by its height
[tex]V_r = 7 * 12 * 19\\\\V_r = 1596\ in^3[/tex]
The volume of the triangular prism is
[tex]V_t = A_b * l[/tex]
Where [tex]A_b[/tex] is the area of the triangular base and l is the length
[tex]A_b = 0.5 * 9 * 12 = 54\ in^2[/tex]
[tex]V_t = 0.54 * 19 = 1026\ in^3[/tex]
Finally
[tex]V = 1596 + 1026[/tex]
[tex]V = 2622\ in ^ 3[/tex]
The answer is:
The total volume is equal to: [tex]2622in^{3}[/tex]
Why?To calculate the total volume of the composite figure, we need to calculate the volume of both of the figures that creates the composite figure.
So, calculating we have:
First figure:
The first figure has a triangular base (side for this case) and height, to find its volume, we just need to calculate the area of its base and then, multiply it by its height.
We are given that:
[tex]base_{height}=9in\\base_{base}=12in\\length=19in[/tex]
Calculating the area of the side/base, we have:
[tex]A=\frac{b*h}{2}[/tex]
[tex]A=\frac{12in*9in}{2}=54in^{2}[/tex]
Now, calculating the volume, we have:
[tex]Volume_{1}=Area*Length\\\\Volume_{1}=54in^{2}*19in=1026in^{3}[/tex]
Second figure:
The second figure is a rectangle, we can calculate its volume using the following formula:
[tex]Volume_2=base*height*width\\\\Volume_2=12in*7in*19in=1596in^{3}[/tex]
Hence, we can calculate the total volume by adding the first volumen and the second volume:
[tex]TotalVolume=Volume_1+Volume_2\\\\TotalVolume=1026in^{3} +1596in^{3}=2622in^{3}[/tex]
The total volume is equal to [tex]2622in^{3}[/tex]
Have a nice day!
Joe spends 18.75% of his working day washing cars. He spends 1.5 hours washing cars. How many total hours does he work per day?
Answer:
8 hours
Step-by-step explanation:
Joe spends 18.75% of his working day washing cars.
Joe spends 1.5 hours washing car.
Therefore 18.75% is equal to 1.5 hour.
18.75% = 1.5 hour
1% = 1.5 ÷ 18.75 = 0.08 hour
100% = 0.08 x 100 = 8 hours
Use technology or a z-score table to answer the question.
Scores on a standardized military exam are normally distributed with a mean of 57 and a standard deviation of 9. Consider a group of 4000 military students.
Approximately how many students will score less than 66 on the test?
A. 200
B. 634
C. 3366
D. 3800
Answer:
C
Step-by-step explanation:
Finding the z-score:
z = (x - μ) / σ
z = (66 - 57) / 9
z = 1
Using a z-score table or calculator:
P(z < 1) = 0.8413
84.13% of 4000 is:
0.8413 (4000) = 3365.2
Rounding up to the nearest whole number, approximately 3366 students will score less than 66. Answer C.
Using the normal distribution, it is found that approximately 3366 students will score less than 66 on the test.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 57, \sigma = 9[/tex]
The proportion of students that scored less than 66 is the p-value of Z when X = 66, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66 - 57}{9}[/tex]
Z = 1
Z = 1 has a p-value of 0.8413.
Out of 4000 students:
0.8413 x 4000 = 3366, which means that option C is correct.
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The graph of y= sin (x-3pi/2) is the graph of the y = sin(x) shifted in which direction?
Answer:
[tex]y=\sin(x-\frac{3\pi}{2})[/tex] is the graph of [tex]y=\sin x[/tex] shifted to the right by [tex]\frac{3\pi}{2}[/tex] units.
Step-by-step explanation:
The given function is
[tex]y=\sin(x-\frac{3\pi}{2})[/tex]
The base function of this trigonometric function is [tex]y=\sin x[/tex]
In general, the transformation [tex]y=\sin(x-k)[/tex] will shift the graph of the base function, [tex]y=\sin x[/tex], k units to the right.
Therefore, [tex]y=\sin(x-\frac{3\pi}{2})[/tex] is the graph of [tex]y=\sin x[/tex] shifted to the right by [tex]\frac{3\pi}{2}[/tex] units.
Answer:
B. 3pi/2 units to the right
Step-by-step explanation:
edge2021
Please help me out....
Answer:
x = 6
Step-by-step explanation:
Given that the line segment is an angle bisector then the following ratios are equal
[tex]\frac{42}{78}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex], that is
[tex]\frac{7}{13}[/tex] = [tex]\frac{6x-1}{10x+5}[/tex] ( cross- multiply )
13(6x - 1) = 7(10x +5) ← distribute parenthesis on both sides
78x - 13 = 70x + 35 ( subtract 70x from both sides )
8x - 13 = 35 ( add 13 to both sides )
8x = 48 ( divide both sides by 8 )
x = 6
Which choice is equivalent to the expression below when y is greater or less than 0?
ANSWER
A. y√y
EXPLANATION
The given expression is:
[tex] \sqrt{ {y}^{3} } + \sqrt{16 {y}^{3} } - 4y \sqrt{y} [/tex]
We factor the perfect square in the first two terms to obtain;
[tex] \sqrt{ {y}^{2} \times y} + \sqrt{ {(4y)}^{2} \times y } - 4y \sqrt{y} [/tex]
This simplifies to:
[tex]y\sqrt{y } + 4y \sqrt{y } - 4y \sqrt{y} [/tex]
We simplify to get;
[tex]y\sqrt{y } + 0 = y \sqrt{y} [/tex]
The correct choice is A.
Write the equation in standard form for the circle with center (9,
-
4) and radius 9.
Answer:
[tex](x-9)^{2}+(y+4)^{2}=81[/tex]
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex](h,k)=(9,-4)[/tex]
[tex]r=9\ units[/tex]
substitute
[tex](x-9)^{2}+(y+4)^{2}=9^{2}[/tex]
[tex](x-9)^{2}+(y+4)^{2}=81[/tex] ----> equation of the circle in standard form
Can someone please help with this question it’s confusing me
The answer might be 2.66
Answer:
0.5
Step-by-step explanation:
12 is the total amount of bags
(2*1/6+ 2*1/3 + 3*1/2 + 4*2/3 + 1*5/6 ) / 12 =
[1/3 + 2/3 + 3/2 + 8/3 + 5/6]/12 = [(1+2+8)/3 + (3*3+5)/6 ]/12 =
(11/3+14/6)/5 = [(22+14)/6 ]/12 = (36/6) /5 = 6/12=0.5
Please help with multiple choice question
The function f(x) = 2x + 5 represents Ken’s earnings working x hours as a waiter. On
3 separate days, he works 2, 8, and 14 hours, representing the domain of the function.
What is the range of f(x)?
a. {4, 16, 28}
b. {–1, 11, 23}
c. {14, 26, 38}
d. {9, 21, 33}
Answer:
D: {9, 21, 33}
Step-by-step explanation:
Ken worked 2, 8 and 14 hours on 3 separate days.
For working 2 hours, his earnings were f(2) = 2(2) + 5, or 9;
For working 8 hours, his earnings were f(28) = 2(8) + 5, or 21; and
For working 14 hours, his earnings were f(14) = 2(14) + 5, or 33
Thus, the range of this function for the days given is {9, 21, 33} (Answer D)
What is the solution to the system of equations?
x+y+3z=-4
2x-z=-3
-x-y-2z=5
a. (-1, -6, 1)
b. (1, -6, 1)
c. (-1, 6, 1)
d. (-1, -6, -1)
Answer:
a
Step-by-step explanation:
Let's use the elimination method on equations 1 and 3 and see what happens:
x + y + 3z = -4
-x - y - 2z = 5
It looks like both the x terms and the y terms cancel out leaving us with the fact that z = 1.
Let's go back to the second equation now and sub in a 1 for z:
2x - z = -3 implies 2x - 1 = -3 and x = -1.
Pick any equation now to sub in the known values to find y. I chose the first one, just because:
x + y + 3z = -4 implies -1 + y + 3(1) = -4 and
-1 + y + 3 = -4 so
y + 2 = -4 and
y = -6
So the solution set is (-1, -6, 1)
The graph shows the number of paintballs a machine launches, y, in x seconds:
A graph titled Rate of Launch is shown. The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line. A line is shown connecting points on ordered pair 2, 12 and 4, 24 and 6, 36 and 8, 48.
Which expression can be used to calculate the rate per second at which the machine launches the balls?
A.) 2/12
B.) 12/2
C.) 2/48
D.) 48/2
Answer:
Option B.) 12/2
Step-by-step explanation:
we know that
The rate of a linear equation is equal to the slope m
The slope is equal to
points (2,12) and (4,24)
m=(24-12)/(4-2)
m=12/2
m=6 balls/sec
PLEASE HELP FAST!
A marble is selected from a bag containing eight marbles numbered 1 to 8.
The number on 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.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
Answer:
A and B: {4, 6}
A or B: {2, 3, 4, 5, 6, 8}
Complement of B: {1, 2, 7, 8}
Step-by-step explanation:
A and B refer to the elements that are in both A and B at the same time
The even numbers from 1 to 8 are {2, 4, 6, 8}
The numbers from 3 to 6 are {3, 4, 5, 6}
Look for the common elements between both sets.
A and B: {4, 6}
A or B is the union of the two sets
Join the elements of both sets
A or B: {2, 3, 4, 5, 6, 8}
The complement of B are all the elements that are not in B.
Write all the elements of the sample space except those of event B
Complement of B: {1, 2, 7, 8}
Event A: 2, 4, 6, 8; Event B: 3, 4, 5, 6.
Explanation:In probability theory, events are outcomes or sets of outcomes from a random experiment. They are subsets of the sample space, representing possible results. Simple events consist of a single outcome, while compound events involve more than one outcome. Probability measures the likelihood of events occurring.
Event A consists of the even numbers 2, 4, 6, and 8.
Event B consists of the numbers 3, 4, 5, and 6.
The outcomes for Event A are 2, 4, 6, and 8.
The outcomes for Event B are 3, 4, 5, and 6.
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Jake cut a round gelatin dessert into 8 equal parts. five of the pieces were eaten . what is the angle measure of the dessert that was left
Answer:
3/8
Step-by-step explanation:
8-5=3
The value of the angle measure of the dessert that was left is equal to
3/8.
We have given that,
Jake cut a round gelatin dessert into 8 equal parts. five of the pieces were eaten.
We have to determine the angle measure of the dessert that was left
What is the angle measure?An angle measure can be defined as the measure of the angle formed by the two rays or arms at a common vertex. Angles are measured in degrees ( °), using a protractor.
Therefore
Jake cut a round gelatin dessert into 8 equal parts is given by,
[tex]\frac{360}{8}=45^0[/tex]
8-5=3
Therefore the angle measure of the dessert that was left is,
[tex]3(45^0)=135^0[/tex]
Therefore the value of the angle measure of the dessert that was left is equal to 3/8.
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what is the surface area of the cube below?
A. 486 units^2
B. 508 units^2
C. 729units^2
D. 405 units^2
Answer:
Correct option is:
A. 486 units²
Step-by-step explanation:
We have to find the surface area of cube with side length 9 units
We know that surface area of cube is:
6s²
where s is the side of the cube
Here, s=9 units
Surface area=6×9×9
= 486 units²
Hence, Correct option is:
A. 486 units²
486 units²
Further explanationGiven:
s = 9 units
Let us find out the surface area of a cube.
The formula of the surface area of a cube is [tex]\boxed{ \ S = 6(s^2) \ }[/tex],
where s is the length of one of the sides.
[tex]\boxed{ \ S = 6(9^2) \ }[/tex]
[tex]\boxed{ \ S = 6(81) \ }[/tex]
[tex]\boxed{ \ S = 6 \times 81 \ }[/tex]
Thus, the surface area of the cube is 486 sq. units.
Notes:
From the formula for surface area, we make it s as a subject.
[tex]\boxed{ \ 6(s^2) = S \ }[/tex]
[tex]\boxed{ \ s^2 = \frac{S}{6} \ }[/tex]
[tex]\boxed{\boxed{ \ s = \sqrt{\frac{S}{6}} \ }}[/tex] ... Equation-1
The formula of the volume of a cube is [tex]\boxed{ \ V = s^3 \ }.[/tex]
Substitute Equation-1 into the volume formula.
[tex]\boxed{ \ V = \bigg( \sqrt{\frac{S}{6}} \bigg)^3 \ }.[/tex]
Thus, we have connected formulas of surface area with the volume of the cube.
Learn moreFind out the area of parallelogram https://brainly.com/question/4459688Find out the area of a trapezoid https://brainly.com/question/2280236Determine the measures of the two angles in a right triangle https://brainly.com/question/4302397#Keywords: what is the surface area of the cube, the length of the cube, volume, 9 units, 486 units², 508 units², 729 units², 405 units², the formula
Which set of steps could be used to solve this story problem? Helen read 4 books per week for the first 3 weeks of her summer vacation. She read 2 books per week for the last 4 weeks. She also read 2 magazines each week. How many books did Helen read over summer vacation? A. Multiply 4 by 3. Then multiply 2 by 4. Add the two products. B. Add 3 and 4. Then add 2 and 4. Add the two sums. C. Multiply 3 × 4. Then add 4 to that product. Then subtract 2. D. Add 4 and 4. Then divide that sum by 2 and add 3 to the quotient.
Answer:
A. Multiply 4 by 3. Then multiply 2 by 4. Add the two products.
Step-by-step explanation:
As with many rate problems, ...
quantity = rate · time
The total quantity will be the sum of quantities associated with different rates or time periods:
total quantity = quantity1 + quantity2
= (rate 1)(time 1) + (rate 2)(time 2)
= (4 books/week)(3 weeks) + (2 books/week)(4 weeks)
= 4·3 books + 2·4 books . . . . . . units of (weeks/weeks) cancel
= (4·3 + 2·4) books . . . . . . formula matches selection A
Find the vertices and foci of the hyperbola with equation quantity x plus 5 squared divided by 36 minus the quantity of y plus 1 squared divided by 64 equals 1.
Vertices: (-1, 3), (-1, -13); Foci: (-1, -13), (-1, 3)
Vertices: (3, -1), (-13, -1); Foci: (-13, -1), (3, -1)
Vertices: (-1, 1), (-1, -11); Foci: (-1, -15), (-1, 5)
Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Answer:
Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)
Step-by-step explanation:
Center at (-5,-1) because of the plus 5 added to the x and the plus 1 added to the y.
a(squared)=36 which means a=6 and a=distance from center to vertices so add and subtract 6 from the x coordinate since this is a horizontal hyperbola, which is (1,-1), (-11,-1). From there you dont need to find the focus since there is only one option for this;
Vertices: (1,-1), (-11, -1); Foci: (-15, -1), (5, -1)
Answer:
Vertices: (1, -1), (-11, -1); Foci: (-15, -1), (5, -1)
Step-by-step explanation:
Ok so we have 5x[tex]\frac{5x^{2} }{36}-\frac{y^{2} }{64}=1[/tex]
As you know we have the equation of the hyperbola as (x-h)^2/a^2-(y-k)^2/b^2, so the formula of the foci is [tex](h+-c,k) and for vertices (h+-a,k)[/tex]
then we have to calculate c using pythagoras theorem we have that
a=6 because is the root of 36
b=8 beacause is the root of 64
And then we have that [tex]c^{2}=a^{2}+b^{2}[/tex]
[tex]c=\sqrt{36+64}[/tex]
So the root of 100 is equal to 10
Hence c=10
Using the formula given before and the equation we know that
h=-5
k=-1
And replacing those values on the equation we have that the foci are
(-5-10, -1)=(-15,-1)(-5+10,1)=(5,-1)And the vertices are:
(-5-6, -1)=(-11,-1)(-5+6, 1)= (1,-1)So the correct answer is D