It will take 5 minutes to paint this cone
How long will it take to paint this cone if it can be painted at the same rate?Since the area of the base of the cone is doubled, the new base area becomes 2 * 49π in² = 98π in².
The radius of the original cone can be found by using the formula for the area of a circle:
49π = πr^2
r = 7 in
The height of the new cone can be calculated using the same lateral height as the original cone:
h = 8 in
Using the formula for the volume of a cone, we can calculate the volume of the new cone:
V = (1/3)πr^2h = (1/3)π(7^2)(8) = (1/3)π(392)
The surface area of the original cone can be found using the formula for the surface area of a cone:
A = πr^2 + πrs
where s is the slant height of the cone.
s = √(r^2 + h^2) = √(7^2 + 8^2) = √(49 + 64) = √(113)
So, we have
A = πr^2 + πrs = π(7^2) + π(7)(√(113)) = 49π + 7π(√(113))
The surface area of the new cone can be found using the same formula:
A = πr^2 + πrs = π(7^2 * 2^2) + π(7 * 2)(√(113)) = 98π + 14π(√(113))
When the equations are compared, we have
2 * 49π + 7π(√(113)) = 98π + 14π(√(113))
Since the new cone has twice the surface area of the original cone and can be painted at the same rate,
It will take 2.5 * 2 = 5 minutes to paint this cone.
Read more about surface area at
https://brainly.com/question/15990299
#SPJ1
Answer:
Step-by-step explanation:
I took the test the answer is 4.2
Yuki and Roman are photographers for the yearbook. Yuki starts with 20 photos. She then takes 60 photos each week. Roman starts with 110 photos. He then takes 35 photos each week. After how many weeks will Yuki and Roman have taken the same number of photos? Write a system of equations that can be used to solve the problem. Write your answers in the blanks.
p = ____________w + ______________
p= ____________w + ______________
After 3 3/5 weeks, they will have the same number of pictures.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, Yuki and Roman are photographers for the yearbook. Yuki starts with 20 photos. She then takes 60 photos each week. Roman starts with 110 photos. He then takes 35 photos each week.
Let "w" the number of weeks they collected the pictures
For Yuki,
The total picture he has after 0 weeks = is 20
The total picture he has after 1 week = 20 + 60
The total picture he has after 2 weeks = 20 + 60*2
The total picture he has after w weeks = 20 + 60*w
For Roman,
The total picture he has after 0 weeks = is 110
The total picture he has after 1 week = 110 + 35
The total picture he has after 2 weeks =110 + 35*2
The total picture he has after w weeks = 110 + 35*w
To calculate the number of weeks when they have equals pictures:
20 + 60*w = 110 + 35*w
25w = 90
w = 3 3/5
Therefore, After 3 3/5 weeks, they will have the same number of pictures.
Learn more about proportionalities here:
https://brainly.com/question/3254974
#SPJ1
Each side of the base of a square pyramid measures 10 inches. The height of each lateral face of the pyramid is also 10 inches.
What is the surface area of the pyramid?
Enter your answer in the box.
The surface area of the square pyramid is given by S = 323.6 inches²
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
Let the surface area of the square pyramid be S
Now , the equation will be
The base of the square pyramid a = 10 inches
The height of the lateral face h = 10 inches
The base area of the pyramid = a²
The lateral surface area of the pyramid = 2a √ ( ( a²/4 ) + h² )
So , the total surface area of square pyramid S = a² + 2a √ ( ( a²/4 ) + h² )
Substituting the values in the equation , we get
The base area of the pyramid = 100 inches²
The lateral surface area of the pyramid = 2 ( 10 ) √ ( ( 100/4 ) + 100 )
On simplifying the equation , we get
The lateral surface area of the pyramid = 223.6 inches²
The total surface area of square pyramid S = 100 inches² + 223.6 inches²
The total surface area of square pyramid S = 323.6 inches²
Hence , the surface area of the pyramid is 323.6 inches²
To learn more about surface area of pyramid click :
https://brainly.com/question/15050758
#SPJ1
A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final
answer to four decimal places and intermediate z-value calculations to two decimal places
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:
0.5874 = 58.74%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953[/tex]
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (18.1 - 17.2)/0.3953
Z = 2.28
Z = 2.28 has a p-value of 0.9887.
Z = (17.1 - 17.2)/0.3953
Z = -0.25
Z = -0.25 has a p-value of 0.4013.
Hence:
0.9887 - 0.4013 = 0.5874 = 58.74%.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
An on-line graphic novel and comic book retailer charges shipping costs according to the following formula
The graph will be piecewise. Then the graph of the function is given below.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
S(n) = 0.50n + 3.5, if 1 ≤ n ≤ 14
S(n) = 0 , if n ≥ 15
The graph will be piecewise. Then the graph of the function is given below.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ1
What the a round the the nearest thousand 802957
12. Which of the following graphs would represent the solution set for y < 6x – 2?
Answer:
YOUR ANDWER MIGHT BE D
Step-by-step explanation:
Solve for x Inscribed Angles.
The value of x is approximately 3.875.
What is inscribed angle and solve x?Given that angle JKL is inscribed in a circle and the measure of angle JKL is (16x-2)°, we can use the property of inscribed angles to find x. Inscribed angles that subtend the same arc have equal measure.
Let's call the measure of angle JKL "m". Then, the measure of angle JKL = m, the measure of angle KJL = m, and the measure of angle JLK = m.
The sum of the angles in a triangle is 180°, so we have:
m + m + m = 180°
3m = 180°
m = 60°
Substituting the value of m into the equation for the measure of angle JKL:
60° = (16x - 2)°
60 = 16x - 2
62 = 16x
x = 3.875
So, the value of x is approximately 3.875.
To learn more about inscribed angle, visit
brainly.com/question/3538263
#SPJ1
what is
5
1/2 plus
2
1/7
A.7 2/9
B.7 5/14
C.7 3/7
D.7 9/14
Which statements about the reflection are true? Check all that apply.
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will remain in the same location as C because it is on the line of reflection.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
The statements that are true are:
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
Options A, B, D, E, and F.
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
Clayton could use the relationship (x, y) → (y, x) to find the points of the image.
This is the y = x reflection rule.
This is true.
Clayton could negate both the x and y values in the points to find the points of the image.
Reflection of (x, y) along the x-axis and y-axis consecutively will give us
(-x, -y).
This is true.
C’ will remain in the same location as C because it is on the line of reflection.
This is not true.
C’ will move because all points move in a reflection.
This is true.
The image and the pre-image will be congruent triangles.
This is true.
The image and pre-image will not have the same orientation because reflections flip figures.
This is true.
Thus,
All statements are true except the statement:
C’ will remain in the same location as C because it is on the line of reflection.
Learn more about reflections here:
https://brainly.com/question/12463306
#SPJ1
Lilianna uses
3
4
4
3
start fraction, 3, divided by, 4, end fraction calories per minute just by sitting. She uses
1
11 more calorie per minute by walking. Lilianna uses a total of
12
1
4
12
4
1
12, start fraction, 1, divided by, 4, end fraction calories walking to the park.
Lilianna uses the equation,
�
(
3
4
+
1
)
=
12
1
4
d(
4
3
+1)=12
4
1
d, left parenthesis, start fraction, 3, divided by, 4, end fraction, plus, 1, right parenthesis, equals, 12, start fraction, 1, divided by, 4, end fraction to represent the situation.
What does the variable
�
dd represent in the equation?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Calories per minute Lilianna uses walking
(Choice B)
B
Number of calories Lilianna would have used sitting
(Choice C)
C
Number of minutes Lilianna walked
Lilianna spend d= 7 minutes total to the park. Therefore, option C is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is d(3/4+1)=12 1/4.
Now, d(3/4+1)= 49/4
d(7/4)=49/4
d=49/4 ×4/7
d= 7
Thus, she spent d= 7 minutes total in the park.
Therefore, option C is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ1
"Your question is incomplete, probably the complete question/missing part is:"
Lilianna uses 3/4 calories per minute just by sitting. She uses 1 more calorie per minute by walking. Liliana uses a total of 12 1/4 calories walking to the park. Lilianna uses the equation, d(3/4+1)=12 1/4 to represent the situation. What does the variable d represent in the equation?
You work for a rock-climbing gym and need to purchase 330 feet of climbing rope to arrive in three days for an event. The online retailer SportsStuff.com charges $5.50 per yard of rope and offers free three-day shipping. The same rope at OutdoorHaven.com costs $5.20 per yard, plus a $12.25 rush delivery fee. What is the cheapest price you can pay for the rope you need for your gym?
Answer:pls brainly award
Step-by-step explanation:
The 330 feet of rope is equivalent to 330/3 = 110 yards.
The cost of the rope at SportsStuff.com is 110 * $5.50 = $605.
The cost of the rope at OutdoorHaven.com is 110 * $5.20 + $12.25 = $604.45.
Therefore, the cheapest price you can pay is $604.45.
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Answer:
The length of the train can be calculated using the formula:
Length of the train = Speed x Time / 2
Where,
Speed = 60 km/hr = 60 x 1000/60 = 1000 m/min
Time = 9 sec = 9 / 60 min = 0.15 min
So,
Length of the train = 1000 x 0.15 / 2 = 75 m
Therefore, the length of the train is 75 meters.
Answer:
Length of the train shold be 75m
Step-by-step explanation:
Identify the range of the relation. {(8,-11), (12, -4), (16, 3), (20, 10)}
Answer:
The range is -11,-4,3,10
Step-by-step explanation:
If tan\alpha =-(2)/(5) and \alpha is in Quadrant IV, find cos\alpha .
The value of cosα is 2/5.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, tanα= -2/5 and α is quadrant IV.
We know that, tan(−θ) = − tan(θ)
α= 2/5
As we know cos(−θ) = cos(θ)
cosα =2/5
Therefore, the value of cosα is 2/5.
Learn more about the trigonometric ratios here:
brainly.com/question/25122825.
#SPJ1
Help
Problems 3.1–3.2
Starting at noon, the temperature changed steadily at a rate of −0.8°C every hour.
At 3 p.m., the temperature was −2.5°C.
What was the temperature at noon?
The temperature at noon is equal to -0.1°C.
What is the slope-intercept form?Mathematically, the standard form or slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Note: Let x represent the time.
Next, we would write an equation that models the situation based on the rate of change (slope) and y-intercept (initial value) as follows;
y = mx + c
y = -0.8x - 2.5
y = -0.8(3) - 2.5
y = -2.4 - 2.5
y = -0.1°C
Read more on rate of change here: brainly.com/question/18569635
#SPJ1
Please help! i have no clue what the answers are!
Answer:
1) 9
2) 27
3) Read explanation below!
Step-by-step explanation:
1) Use the Pythagorean theorem to find AD. Show your working
Pythagorean theorem = a²+b²=c²Where a = 12 and c=15 = 12²+?²=15²To find '?' we first have to expand the indices...
12² = 14415² = 225144 + ?² = 225Now work out '?'
225 - 144 = 81√81 = 92) Find AC. Show your working
We have found out that AD is 9 and to find AC we have to add 18!
9 + 18 = 273) Is ΔABC a right triangle? Explain
We can that ΔABC is not a right angle as none of the angles in the triangle are 90°! If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!
Have a lovely day :)
You own Company X. When you started the company, you Initially invested $12,000. You also borrowed $12,000 through a five-year (long-term) loan, of which you have paid back $2,018. You have retained $1,291 in earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term investment. The company owns land and a building worth $8,878 and equipment worth $4,230. As of today, the company has $8,250 in cash, $1,225 in Inventory, and is due to receive accounts worth $675. However, the company owes its suppliers $485 and has a $500 loan to pay off in the next six months.
The equity of Company X's is $13,291.
What is the equity?The difference between assets and liabilities is the equity.
The equity is the portion of assets belonging to the owners.
Analysis:Initial investment = $12,000
Retained Earnings = $1,291
Long-term loan = $9,982 ($12,000 - $2,018)
Land and building = $8,878
Equipment = $4,230
Cash $8,250
Inventory = $1,225
Accounts Receivable = $675
Accounts Payable = $485
Short-term loan = $500
Company X
Balance SheetAs of current date
Current Assets:Cash $8,250
Inventory 1,225
Accounts Receivable 675 $10,150
Long-term Assets:Long-term investment $1,000
Land and building 8,878
Equipment 4,230 $14,108
Total Assets $24,258
Current Liabilities:Accounts Payable $485
Short-term loan 500 $985
Long-term Liabilities:Long-term loan $9,982
Total liabilities $10,967
Equity:Initial capital $12,000
Retained earnings 1,291 $13,291
Total liabilities and equity $24,258
Learn more about the equity at https://brainly.com/question/14032844
#SPJ1
Question Completion:Determine Company X's equity?
A scout troop took a camping trip to the dunes that lasted for 97 minutes. Along the way, they stopped
at 10:48AM for a break. The troop didn't check the time when they left, but when they arrived a park
ranger said it was 11:37AM. What time did they start the trip?
Answer:
they started trip at 10:00 am
Step-by-step explanation:
Let's call the starting time "S".
The arrival time is 11:37AM,
difference in time after break to park arrived : 11:37 am - 10:48 am = 49 minutes
remaining time : 97-49= 48 minutes
starting time= 10:48 am -48 minutes = 10:00 am
Write an equation of the line in POINT-SLOPE form that passes through the given points.
(5,-1) and (-3,-4)
(Type an EQUATION. Simplify your answer.)
The equation the line is, y = 3/8 *x - 23/8, equation of the line in POINT-SLOPE form that passes through the given points (5,-1) and (-3,-4).
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (5,-1) and (-3,-4)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
now, solving we get,
3x-8y = 23
equation of the line in POINT-SLOPE form is,
y = 3/8 *x - 23/8
Hence, the required equation is, y = 3/8 *x - 23/8
To learn more on Equation 0f Straight-Line click:
brainly.com/question/11116168
#SPJ1
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without
replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics
Company has just manufactured 1650 write-rewrite CDs, and 60 are defective. If 3 of these CDs are randomly
selected for testing, what is the probability that the entire batch will be accepted?
Rounded to four decimal place accuracy.
Submit Question
Therefore , the solution of the given problem of probability comes out to be likelihood that the full batch will be approved is therefore 0.832.
What does the probability procedure entail in detail?Probability theory is an area of mathematics that focuses on calculating the probability that a claim is accurate or that a particular occurrence will occur. Chance can be represented by any number range between 0 and 1, where 1 often denotes certainty and 0 typically denotes possibility. A probability diagram shows the possibility that a specific event will occur. The numerals 0 and 1, fractions with a ranging of 0% to 100%, or a few more characters can all be used to indicate probabilities.
Here,
Given that we've done it
Amount of CDs: 2100
50 faulty CDs total.
If every component of the sample is acceptable, the complete batch is accepted.
Therefore, we shall apply the "Binomial Theorem"
If there is no flaw, let p be the likelihood of success.
So, => p = 2100 - 50 / 2100
=> p = 2050/2100
=> p =0.97
q is the likelihood of a failure, or defect.
So,
=> q = 50/2100
=> q = 0.02
hence, the number of CDs chosen is 6.
Consequently, it is => P(X=6) = (0.97)6 = 0.832.
The likelihood that the full batch will be approved is therefore 0.832.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
Three straight lines are shown in the diagram. Work out the sizes of angles a,b and c.
15 points to whoever gets this by the way.
Answer:
see below
Step-by-step explanation:
a=50 because it's cut out of a full circle = 360, and it tells you what's left = 310
so 360-310=50
In a survey of 290 newspaper readers, Isl of them read the daily times, 142 read the Guardian, 117 read punch and each read at least one of the three papers. If 75 read the Daily Times and the Guardian, 60 read the Daily times and Punch, and 54 read the Guardian and punch (a) draw a Venn diagram to illustrate this Information (b) How many readers read (I) All three papers (ii) exactly two of the papers. (iii) exactly one of the papers. (iv) The Guardian alone?
In Venn diagram All three papers 39,exactly two of the papers 189, exactly one of the papers 251 and The Guardian alone 142.
How is a Venn diagram explained?A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.
They frequently serve to visually group objects while highlighting how they differ and how they are similar.
(I) All three papers
(G∪P∪T) = G + P+T+G∩P+G∩T+P∩T-(G∩P∩T)
290=142+181+117+75+60+54-(G∩P∩T)
(G∩P∩T)=39
(ii) exactly two of the papers = 60+75+54=189
(iii) exactly one of the papers =251
(iv) The Guardian alone =142.
To know more about Venn diagram visit:-
https://brainly.com/question/29301560
#SPJ1
Given the following composite figures, d=8.6 cm and w=12.5 cm. What is the perimeter of the figure?
a. The perimeter of the figure is: 61.4 cm
b. The area of the figure is: 160.69 cm²
How to Find the Perimeter and Area of a Figure?The figure consists of two semicircles which makes one full circle and a rectangle. Therefore:
a. The perimeter of the given figure = circumference of a circle + 2w.
d = 8.6 cm
Circumference of the circle = 2 * pi * r = 2 * 3.14 * (8.6/2) = 27.00 cm
Perimeter = 27.00 + 2(17.2)
Perimeter = 61.4 cm
b. Area = area of circle + area of rectangle = 2πr + (length * width)
r = 7.9/2 = 3.95 cm
length = w = 17.2 cm
width = d = 7.9 cm
Area = 2*3.14*3.95 + (17.2*7.9) = 160.69 cm²
Learn more about the area and perimeter of a figure on:
https://brainly.com/question/443376
#SPJ1
A recipe uses 3 cups of milk to make 9 servings. If the same amount of milk is used
for each serving, how many servings can be made from two quarts?
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup
8 fluid ounces
Before you try that problem, answer the question below.
How many cups will you need to find the number of
servings for?
The servings that can be made from two quarts is 24
How many servings can be made from two quarts?To convert the recipe's milk measurement from cups to quarts,
We first need to determine how many cups are in a quart.
There are 4 cups in a quart.
So, 3 cups of milk is equivalent to
3 / 4 = 0.75 quarts of milk.
Since the recipe uses 0.75 quarts of milk to make 9 servings,
Then each serving uses 0.75 / 9 = 0.083 quarts of milk.
Now, 2 quarts of milk is equivalent to 2 / 0.083 = 24 servings.
Therefore, from two quarts of milk, 24 servings can be made using this recipe.
Read more about rate at
https://brainly.com/question/24178013
#SPJ1
A construction worker earned $17 per hour for the first 40 hr of work and $25.50 per hour
for work in excess of 40 hr.
(a)Write a function to model her weekly pay W in terms of the number of hours she
worked that week.
(b) One week she earned $896.75. How much overtime did she work?
Answer:
Step-by-step explanation:
W(40)x25
Mathmatics for Calculus
This is a problem finding the slope of a line at some point "a"
It accomplishes this by doing an average rate of change formula over an area approaching 0.
We must know the format of this type of equation.
See first image.
The variables in this example don't match up.
Let the function input be x, and the limit being a --> 0
a = 2
f(x) = x^5
Answer:
[tex]\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}[/tex]
Step-by-step explanation:
The first principal of derivative:
[tex]\displaystyle{f'(x) = \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}}[/tex]
Since the given problem represents f'(a), meaning:
[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}[/tex]
If we compare:
[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}[/tex]
and
[tex]\displaystyle{ \lim_{h\to 0} \dfrac{(2+h)^4-16}{h}}[/tex]
which can be rewriten as:
[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{(2+h)^4-2^4}{h}}[/tex]
We can conclude by comparing that:
a = 2f(2) = 2⁴This would mean that:
[tex]\displaystyle{f(x)=x^4}[/tex]
Therefore:
[tex]\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}[/tex]
If 2 equals m then what is 3m+5
Answer: 11
Step-by-step explanation:
3x2=6
6+5=11
What is the least number that two whole numbers can have as the LCM? A. the greater of the two numbers the lesser of the two numbers B. C. the product of the two numbers D. the sum of the two numbers
Answer:
b
Step-by-step explanation:
:)
The table shows the number of game tickets and the number of ride tickets purchased by 3 friends at a state fair. Complete the table to determine the total amount spent on tickets by Edgar.
The total amount spent on tickets by Edgar is $15.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the cost of one game ticket and y be the cost of one ride ticket.
From the table, we can form two linear equations regarding the total amount spent by Erica and Penny.
10x + 5y = 10
15x + 10y = 16.25
Multiplying the first equation throughout with 2,
20x + 10y = 20
Subtracting 15x + 10y = 16.25 from the above equation,
(20x + 10y) - (15x + 10y) = 20 - 16.25
5x = 3.75
x = 0.75
Substituting x = 0.75 in 10x + 5y = 10,
7.5 + 5y = 10
5y = 2.5
y = 0.5
Cost of a game ticket is $0.75 and cost of a ride ticket is $0.50.
Total cost by Edgar = (12 × 0.75) + (12 × 0.5) = $15
Hence the total money spent by Edgar for both game and ride tickets is $15.
Learn more about Linear Equations here :
https://brainly.com/question/11897796
#SPJ1
NO LINKS!!!!
A city government has approved the construction of an $800 million sports arena. Up to $480 million will be raised by selling bonds that pay simple interest at a rate of 7% annually. The remaining amount (up to $640 million) will be obtained by borrowing money from an insurance company at a simple interest rate of 2%. Determine whether the arena can be financed at the annual interest rate is $32 million.
The arena should be financed by selling $________ million in bonds and borrowing $__________ million.
The arena should be financed by selling $ 320 million in bonds and borrowing $ 480 million.
==========================================================
Work Shown:
x = amount (in millions of dollars) from bonds at 7% interest rate.y = amount (in millions of dollars) borrowed at 2% interest rate.Something like x = 27 means "27 million dollars of bonds were sold".
The variable x has the restriction of [tex]0 \le x \le 480[/tex] since $480 million is the ceiling for the bonds.
The variable y has the restriction of [tex]0 \le y \le 640[/tex] since $640 million is the ceiling for the money borrowed from the insurance company.
The two amounts, x and y, must add to 800 to represent the $800 million total that needs to be raised.
x+y = 800
y = 800-x
-------------------
Let's calculate the interest for each item. Use the simple interest formula.
Bonds at 7% interest rate:
i = P*r*t
i = x*0.07*1
i = 0.07x
Borrowed money at 2% interest rate:
i = P*r*t
i = y*0.02*1
i = 0.02y
Total annual interest = 0.07x+0.02y = 32
The 32 at the end represents the $32 million of interest payout. This amount of money is paid to the bondholders and to the insurance company, and is done so yearly.
-------------------
Apply substitution to solve for x.
0.07x+0.02y = 32
0.07x+0.02(800-x) = 32 ...... plug in y = 800-x
0.07x+16-0.02x = 32
0.05x+16 = 32
0.05x = 32-16
0.05x = 16
x = 16/(0.05)
x = 320
They should sell $320 million in bonds.
320 million = 320,000,000
Note how x = 320 is in the interval [tex]0 \le x \le 480[/tex]
y = 800-x
y = 800-320
y = 480
They should borrow $480 million at an interest rate of 2%
480 million = 480,000,000
Note how y = 480 is in the interval [tex]0 \le y \le 640[/tex]
Answer:
The arena should be financed by selling $320 million in bonds and borrowing $480 million.
Step-by-step explanation:
Simple interest is calculated by multiplying the principal by the interest rate (in decimal form) and the time (in years).
Let x be the amount raised by selling bonds that pay an annual simple interest rate of 7%.
Therefore:
Interest = 0.07x
As the total cost of the sports arena is $800 million, the amount raised from borrowing money from the insurance company at an annual simple interest rate of 2% is (800 - x). Therefore:
Interest = 0.02(800 - x)To determine whether the arena can be financed so that the annual interest is $32 million, equate the sum of the two expressions for interest to 32 and solve for x:
[tex]\implies 0.07x+0.02(800-x)=32[/tex]
[tex]\implies 0.07x+16-0.02x=32[/tex]
[tex]\implies 0.05x+16=32[/tex]
[tex]\implies 0.05x=16[/tex]
[tex]\implies x=320[/tex]
As x is the amount raised by selling bonds, then the amount in bonds that should be sold is $320 million.
To calculate the amount to borrow, subtract the amount in bonds sold from $800 million:
[tex]\implies 800-320=480[/tex]
Therefore, the amount to be borrowed from an insurance company is $480 million.
As both these amounts are less than the maximum limits set, they are both valid.