For the standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.
Define the term area?The amount of cardboard needed to make a banner depends on the size of the banner. If we know the dimensions of the banner, we can calculate the area of cardboard needed.
Assuming that the banner is a rectangle, let's say its width is w inches and its height is h inches.
Then, the area of the banner can be calculated as:
Area = width x height
Area = w x h
To find out how many square inches of cardboard are needed, we need to add a margin to the dimensions of the banner to account for the thickness of the cardboard. Let's say the margin is m inches.
Then, the width of the cardboard needed is (w + 2m) inches, and the height of the cardboard needed is (h + 2m) inches.
The area of the cardboard needed can be calculated as:
Area of cardboard = (width of cardboard) x (height of cardboard)
Area of cardboard = (w + 2m) x (h + 2m)
So, the total area of cardboard needed for one banner is:
Total area of cardboard = Area of cardboard + Area of margin
Total area of cardboard = (w + 2m) x (h + 2m) + 4m(w + h + 2m)
if we assume that the banner is 2 feet wide (24 inches) and 4 feet long (48 inches), and we add a margin of 1 inch on each side, then we can calculate the total area of cardboard needed as follows:
Total area of cardboard = (24 + 2) x (48 + 2) + 4(1)(24 + 48 + 2)
Total area of cardboard = 26 x 50 + 4(74)
Total area of cardboard = 1300 + 296
Total area of cardboard = 1596 square inches
So, for this standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.
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If the radius of Sphere B is 5 times larger than the radius of Sphere A, how many times larger is the volume of Sphere B compared to that of Sphere A?
The volume of Sphere A is V(A) = (4/3)πr³ and the volume of Sphere B is V(B) = 125(4/3)πr³. So the volume of Sphere B is 125/1 = 125 times larger than that of Sphere A.
what is sphere?
A sphere is a three-dimensional geometric shape that is perfectly round, like a ball. It is defined as the set of all points in space that are equidistant from a given point, called the center of the sphere.
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.
Let the radius of Sphere A be denoted by "r", then the radius of Sphere B is 5r.
The volume of Sphere A is V(A) = (4/3)πr³.
The volume of Sphere B is V(B) = (4/3)π(5r)³ = (4/3)π125r³ = 5³(4/3)πr³ = 125(4/3)πr³.
Therefore, the volume of Sphere B is 125/1 = 125 times larger than that of Sphere A.
So, the volume of Sphere B is 125 times larger than that of Sphere A.
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Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places. X y
2 8. 18
6. 5 12. 816
11 16. 768
15. 5 21. 222
20 26. 462
24. 5 31. 36
29 34. 584
y
=
x
+
The missing coefficients in the equation y = mx + b are m = 0.841 and b = 18.813. The final equation that fits the given data is y = 0.841x + 18.813
To find the missing coefficients in the equation y = mx + b, we need to use the given data in the table to determine the values of m and b.
We can start by using two of the data points to set up a system of equations:
Using (5, 23.018) and (6, 23.859):
m(5) + b = 23.018
m(6) + b = 23.859
Subtracting the first equation from the second equation gives:
m(6) - m(5) = 0.841
Simplifying this expression:
m = 0.841 / (6 - 5) = 0.841
Now we can substitute the value of m into one of the original equations to solve for b:
m(5) + b = 23.018
0.841(5) + b = 23.018
b = 23.018 - 4.205
b = 18.813
Therefore, the missing coefficients are:
m = 0.841
b = 18.813
The equation y = 0.841x + 18.813 fits the given data.
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The given question is incomplete, the complete question is:
Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places. X y 5 23.018 5.5 23.438 6 23.859 6.5 24.035 7 25.449 7.5 24.868 8 26.058 I Enter an integer or decimal number [more..] y = I+
A car dealer has 20 Toyota Camrys and 25 Honda Accords left on the parking lot. The dealer wants to arrange the cars in rows so that each row has the same number of vehicles and the same number of vehicles of each type. What is the greatest number of rows that can be formed?
There will be __ rows with __ Toyota Camrys and __Honda Accords in each row.
Miller is going to install baseboard around the perimeter of her room's rectangular floor, shown below. The floor has dimensions 15 feet by 20 feet. The 2 doorways in her room are each 3 feet wide and do not require baseboard. Assuming an average cost of $0.30 per linear foot requiring baseboard, how much will it cost Naomi to purchase baseboard for her room? Use the CER strategy to explain your answer.
If Miller is going to install baseboard around the perimeter of her room's rectangular floor, s. it will cost Miller $19.20 to purchase baseboard for her room, assuming an average cost of $0.30 per linear foot requiring baseboard.
What is the cost price?To find out how much it will cost Miller to purchase baseboard for her room, we can use the CER (Conversion, Equation, and Re-substitution) strategy.
Conversion:
We can calculate the perimeter of the room by adding the lengths of all four sides:
Perimeter = 2(Length + Width) - 2(Doorway Width)
Perimeter = 2(15 + 20) - 2(3)
Perimeter = 64 feet
So, Miller will need 64 feet of baseboard.
Equation:
To calculate the cost of the baseboard, we can use the formula:
Cost = Length * Cost per linear foot
In this case, the length is 64 feet and the cost per linear foot is $0.30.
Cost = 64 * 0.30
Cost = $19.20
Therefore the final answer is that it will cost Miller $19.20 to purchase baseboard for her room, assuming an average cost of $0.30 per linear foot requiring baseboard.
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Greg set a goal of raising enough money to buy a new bicycle that cost $210 he has already re-$60 and he will earn $15 for each long that he mows this summer which number line represents the number of lawns can mow and meet his goal?
Option 1 is correct, The point will be on 10 for the cost $240.
=> 0—————————-10—————————-20
An unitary methοd is what?By multiplying the data οbtained with such a nanοsectiοn variable whilst alsο twο that used the unitary methοd , the jοb can be finished. In essence, this mean that whenever a desired item appears, the specified entity is set οr the cοlοur space οf bοth prοductiοn runs is skipped. A varying fee οf Inr ($1.01) might have been necessary fοr fοrty pens.
Here,
Greg wants tο cοllect enοugh cash tο spend $210 οn a new bicycle. He needs tο make an extra $150 because he already has $60. He needs tο mοw the fοllοwing lawns in οrder tο make his $15 per lawn:
=> 150 ÷ 15 = 10 acres
Greg must mοw at least 10 yards in οrder tο accοmplish his οbjective. The number line shοwing hοw many fields he can mοw is as fοllοws:
=> 0—————————-10—————————-20
The number οf lawns he can mοw tο reach his οbjective is represented by any value οn this number line larger than οr equal tο 10. He will, fοr instance, be cοmpensated:
=> 12 × $15 = $180
He already has $60, sο after adding this, he will have:
=> $60 + $180 = $240
which will cοver the cοst οf the new mοtοrbike.
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3. Consider the quadratic equation x2 + 2x - 35 = 0. Solve by factoring and using the zero-product property. What are solutions to quadratic equations called? Show your work.
To solve the equation, factor [tex]\bold{x^2+2x-35}[/tex] use the formula [tex]\bold{x^2 +(a + b) x + ab = (x + a)(x + b)}[/tex]. To find a and b, set up a system to be solved.
[tex]a + b = 2[/tex]
[tex]ab = -35[/tex]
Since ab is negative, a and b have opposite signs. Since [tex]a+b[/tex] is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.
[tex]\bold{-1.35}[/tex][tex]\bold{-5.7}[/tex]Calculate the sum of each pair.
[tex]\bold{-1 + 35 = 34}[/tex][tex]\bold{-5 + 7 = 2}[/tex]The solution is the pair that gives sum 2.
[tex]\bold{a = -5}[/tex][tex]\bold{b = 7}[/tex]Rewrite the factored expression [tex](x + a)(x + b)[/tex] with the values obtained.
[tex]\bold{(x -5)(x + 7)}[/tex]To find solutions to equations, solve [tex]x-5=0[/tex] and [tex]x+7=0[/tex].
[tex]\bold{x = 5}[/tex][tex]\bold{x = -7}[/tex]What are the solutions of quadratic equations called?The "solutions" of a Quadratic Equation are the values where the equation equals zero. They are also called "roots", or even "zeros".
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Problem #2 (15 Points)
2. A report by a tourism company says that 28% of United States citizens plan to travel
internationally annually. The tourism company selects a random sample of 40 people and
calculates the sample proportion (p) of people planning to travel internationally.
a. Tell whether n-p≥10 and n-(1 p)≥10 are true or false.
F +
+Show your work here:
-
b. Describe the shape of the sampling distribution of the sample proportion of people
who expect to travel internationally the next year. Write an explanation for your
reasoning.
Show your work here:
Answer:
Step-by-step explanation:
its b
Find the slope of the line that passes through the pair of points (7/20,5/19)and 5/9,11/16)
The slope of the line that passes through the pair of points (7/20,5/19) and (5/9,11/16) is 3/5.
To find the slope of a line passing through two points, we need to use the slope formula. The slope formula is m = (y2 - y1) / (x2 - x1). To calculate the slope, we need to first calculate the x and y values of the two points, (7/20,5/19) and (5/9,11/16). The x values are 7/20 and 5/9 and the y values are 5/19 and 11/16. We can then plug these values into the slope formula to get the slope. The slope is (11/16 - 5/19) / (5/9 - 7/20) = 3/5. Therefore, the slope of the line that passes through the two points (7/20,5/19) and (5/9,11/16) is 3/5.
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what is the slope from (-4,6) to (2, 3/2)?
Answer:
1\2
Step-by-step explanation:
Suppose that a factory produces light bulbs, and the percentage of defective bulbs is 3.5% . If a sample of 550 light bulbs is selected at random what is the probability that the number of defective bulbs in the sample is greater than 15
probability-=0.3419
The probability that the number of defective bulbs in a sample of 550 light bulbs is greater than 15 is 0.3419. To calculate this probability, you need to use the binomial probability formula: P(x) = nCx * p^x * q^(n-x), where n is the sample size (550), p is the probability of a defective bulb (0.035), x is the number of defective bulbs you want to calculate (15) and q is the probability of a non-defective bulb (1-0.035). Plugging in the values, we get P(x) = 550C15 * 0.035^15 * 0.965^(550-15) = 0.3419
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Which value of x is the solution to this equation? 5x2 = 30x – 45
Answer:
x = 11/6 or 1 5/6 or 1.83333...
Step-by-step explanation:
The solution to the equation 5x^2 = 30x – 45 is x = 3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have the Equation: 5x² = 30x - 45.
We can start by simplifying the equation by subtracting 30x and adding 45 from both sides to get:
5x² - 30x + 45 = 0
We can further simplify by dividing both sides by 5 to get:
x² - 6x + 9 = 0
This can be factored as (x - 3)(x - 3) = 0, which means that the only solution is x = 3.
Therefore, the solution to the equation 5x^2 = 30x – 45 is x = 3.
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What is the value x + y? (Round your answer to the nearest tenth)
Answer:
x + y = 110
Step-by-step explanation:
[tex]x=\sqrt{(65^{2} - 56^{2} } \\x=33\\\\\\y=\sqrt{(85^2-36^2} \\y=77\\\\x+y=33+77\\x+y=110[/tex]
What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or
leave in terms of π. Show your work.
As a result, the answer to the following question, As a result, the supplied radius arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).
what is radius?In more modern use, the length of a sphere or sphere is equal to its radius in standard geometric, so it has several line segments from its centre to its circumference. The phrase is derived from the Latin word for radius, which also referred to the spokes of a waggon wheel. The radius of a circle is the distance between the centre and any point on its periphery. Often, "R" or "r" is used to signify it. A radius is a boundary line with one terminus in the centre and a second around the perimeter of a circle. Vide letter diameter equals radius The dimension of a circle is the segment that passes its centre and has extremities that are on the circle.
The formula for calculating the arc length of a circle is:
Arc length = radius x central angle in radians,
In order to use this formula, we must first convert the centre angle from degrees to radians. We are aware of the following:
2 radians Equals 360 degrees
360 degrees divided by 2 radians equals x degrees divided by y radians
(x degrees * 2 radians) / 360 degrees = y
y = (22 deg * 2 radians) / 360 deg = 0.38397 deg (rounded to five decimal places)
arc length Equals radius multiplied by Centre angle in radians
With r = 18 inches and = 0.38397 radians, we get:
arc length = 18 inches multiplied by 0.38397 equals 6.9115 inches (rounded to four decimal places)
As a result, the supplied arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).
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Work out 2 and 1/2 x 1 and 4/5
Give your answer as a mixed number in its simplest form
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
Can someone show me an example on how to solve a y=mx+b equation?
Answer:
hey, good afternoon!
Step-by-step explanation:
here is an example: the cost of a pizza is 7.50 and you can add a topping for 0.65 cents. find the cost of the pizza with 6 toppings
y=mx+b
the x stands for the toppings and y is the cost. the rate is 0.65 cents and the orginal amount of money is b. so the equation would look like this:
y= .65x+7.50. x=6
y = 65(6)+7.50
=3.9+ 7.50= $11.50(answer)
the m is the rate of change in this question is 0.65 cents
b is initial/ fixed/ value once again in this qeustion it 7.50$
hope this helps. have a great day!
A man of mass 60kg runs with a constant velocity. He has kinetic energy of 750j. Calculate his velocity
Answer:
the velocity of the man is 5 m/s.
Step-by-step explanation:
The kinetic energy of a moving object is given by the equation:
K.E. = 0.5 * m * v^2
where
K.E. is the kinetic energy
m is the mass of the object
v is the velocity of the object
In this problem, we are given that the man has a mass of 60 kg and a kinetic energy of 750 J.
So,
750 J = 0.5 * 60 kg * v^2
Solving for v:
v^2 = (2 * 750 J) / 60 kg
v^2 = 25 J/kg
v = sqrt(25 J/kg)
v = 5 m/s
Therefore, the velocity of the man is 5 m/s.
A bag contains marbles 3 red, 4 green, and 5 white. If a marble is pulled from the bag what is the probability it will be green
If a bag contains 3 red, 4 green, and 5 white marbles, then the probability that a green marble will be selected in the first attempt is equal to 4/12 or 1/3.
Probability is defined as the likeliness of an event to happen. It simply means possibility of any event to occur or the possibility of an event to not occur. The sum of the possibilities in any event is always equal to one. In the given case, there are 3 red, 4 green, and 5 white marbles.
Now total number of marbles is equal to 3+4+5 = 12 marbles
Probability that the green marble is picked first = 4/12 = 1/3
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Which research scenario would most likely be biased against non-voters? Select all that apply.
1. a convenience sample collected at a political rally used to determine candidate preferences
2. a volunteer sample collected at a political rally used to determine candidate preferences
3. a simple random sample of all non-voters used to determine why they don’t vote
4. a simple random sample of all eligible voters, some of whom didn’t have time to vote
5. a volunteer sample collected at large department store to determine who they voted for
The scenariο that wοuld mοst likely be biased against nοn-vοters is a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences
What is a biased expressiοn?A cοgnitive bias clοuds οur critical thinking and may result in the spread οf false infοrmatiοn that may be harmful tο οther peοple. Biases cause us tο avοid infοrmatiοn that might be uncοmfοrtable οr unwelcοme rather than lοοking intο the infοrmatiοn that might help us reach a mοre accurate cοnclusiοn.
A cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences is nοt a biased sample. Since the nοn-vοters are nοt
A vοlunteer sample cοllected at a pοlitical rally was used tο determine candidate preferences. It prefers a particular member. This is a biased survey.
A simple randοm sample οf all nοn-vοters was used tο determine why they dοn’t vοte. It is biased. Because a grοup οf peοple decides nοt tο give a vοte.
A simple randοm sample οf all eligible vοters, sοme οf whοm didn’t have time tο vοte. It is a sample.
A vοlunteer sample was cοllected at a large department stοre tο determine whο they vοted fοr. It is a nοn-biased survery. The peοple dο nοt prefer a particular team.
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A hardware store charges a $40 rental fee and
$20 per day to rent a power washer. Which
equation correctly relates the total cost y to rent the
washer for x days? 8. F. 1-3
A. Y=20+40x. B. Y=40+20x
C. Y=40 -x/20.
D. Y=20 -x/ 40.
The equation correctly relates the total cost y to rent the washer for x days is option (B) Y = 40 + 20x
The rental fee of $40 is charged regardless of the number of days the power washer is rented. In addition to this fee, there is a daily charge of $20 per day.
Therefore, the total cost of renting the power washer for x days can be calculated by multiplying the daily charge by the number of days rented and adding the rental fee:
Total cost = (daily charge) x (number of days rented) + rental fee
Total cost = $20x + $40
This linear equation can be rearranged to the form:
Y = 40 + 20x
Therefore, the correct option is (B) Y = 40 + 20x
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What will be one-fifth of a complete angle in degrees
Answer:
72 degrees
Step-by-step explanation:
If a complete angle is 360 degrees, one-fifth of a complete angle would be:
360 ÷ 5 = 72Therefore one-fifth of a complete angle is 72 degrees.
answers for these please
The values of the variables are x = 2, z = 6.92, x = 10.5 and y = 12.6
How to find the values of the variablesFigure 12
In this figure, we make use of the following theorem of intersecting secants
AB * AC = AD * AE
By substitution, we have
(x + 4) * (x + 4 + x - 2) = 4 * 9
Evaluate the sum
(x + 4) * (2x + 2) = 36
So, we have
(x + 4) * (x + 1) = 18
Expand
x^2 + 5x + 4 = 18
Evaluate the like terms
x^2 + 5x - 14 = 0
Factorize
(x + 7)(x - 2) = 0
Solve for x
x = -7 or x = 2
x cannot be negative
So, we have
x = 2
Figure 13
In this figure, we make use of the following theorem of intersecting secant-tangent
XU * WU = UV^2
So, we have
8 * 6 = z^2
Evaluate
z^2 = 48
Take the square root
z = 6.92
Figure 14
Using the same theorem used in (13), we have
2 * (2 + x) = 5^2
So, we have
4 + 2x = 25
Evaluate
2x = 21
Divide
x = 10.5
Figure 15
Using the same theorem used above
y^2 = 8 * 20
So, we have
y^2 = 160
Take the square root
y = 12.6
Hence, the value of y is 12.6
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Harry, Jason and Sarah are taking the GMAT which is required by most applicants for admission to graduate schools of business. The three friends want to get admissions to three different business schools. Harry can get the admission if he gets a score above 650 in GMAT, Jason can get the admission if he gets above 630 and Sarah can get the admission if she gets above 670. Scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115. What is the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another.
Probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.
The probability of Harry, Jason, and Sarah getting admission to their desired schools is the probability that Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670. The scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115.So, let's first standardize Harry's score:Z = (650 - 550) / 115 = 0.87Similarly, for Jason's score:Z = (630 - 550) / 115 = 0.70And for Sarah's score:Z = (670 - 550) / 115 = 1.04Now we need to find the probabilities of getting each of these Z-values. We can do that using the standard normal distribution table. The table gives the probability that a standard normal random variable is less than or equal to a certain Z-value.To find the probability that Harry's score is above 650, we need to find the probability that Z > 0.87. This can be found by subtracting the probability of Z ≤ 0.87 from 1:P(Z > 0.87) = 1 - P(Z ≤ 0.87) = 1 - 0.8078 = 0.1922Similarly, the probability that Jason's score is above 630 is:P(Z > 0.70) = 1 - P(Z ≤ 0.70) = 1 - 0.7580 = 0.2420And the probability that Sarah's score is above 670 is:P(Z > 1.04) = 1 - P(Z ≤ 1.04) = 1 - 0.8508 = 0.1492The probability that all three events occur (Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670) is the product of their probabilities:P(Harry, Jason, and Sarah) = P(Z > 0.87) × P(Z > 0.70) × P(Z > 1.04) = 0.1922 × 0.2420 × 0.1492 = 0.0088Therefore, the probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.
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On her math homework, Emely got 13 questions correct for every 7 questions she got wrong. What percentage of her math homework questions did Emely get wrong?
Emely gοt 35% οf her math hοmewοrk questiοns wrοng.
What is the percentage?A percentage that represents a tenth οf a quantity. One percent, denοted by the symbοl 1%, is equal tο οne-hundredth οf sοmething; hence, 100 percent denοtes the full thing, and 200 percent designates twice the amοunt specified. A pοrtiοn per hundred is what the percentage denοtes. The percentage refers tο οne in a hundred. The % sign is used tο denοte it.
Emely gοt 13 questiοns cοrrect fοr every 7 questiοns she gοt wrοng.
We can start by finding the fractiοn οf questiοns Emely gοt wrοng, which is 7/(7+13) = 7/20. Tο cοnvert this tο a percentage, we can multiply by 100 tο get 35%.
Therefore, Emely got 35% of her math homework questions wrong.
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What is the interest on a $1,000, 18-month loan, with a 10% simple interest rate?
Answer:
$150
Step-by-step explanation:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the interest rate, and Time is the duration of the loan.
In this case, the Principal is $1,000, the Rate is 10%, and the Time is 18 months (which we'll convert to a fraction of a year).
First, we need to convert 18 months to a fraction of a year. Since there are 12 months in a year, 18 months is equal to 18/12 = 1.5 years.
Using the formula:
Interest = Principal x Rate x Time
Interest = $1,000 x 0.10 x 1.5
Interest = $150
So the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.
Answer:
The formula for simple interest is I = Prt, where I is the interest, P is the principal or amount borrowed, r is the interest rate, and t is the time in years.
In this case, P = $1,000, r = 10% or 0.10 as a decimal, and t = 1.5 years (since 18 months is equivalent to 1.5 years).
I = Prt
I = $1,000 * 0.10 * 1.5
I = $150
Therefore, the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.
Find each Measure. 15 points
Answer:
M<E = 63
M<F = 63
M<G = 117
Step-by-step explanation:
M<F:
= 180-117
=63
M<E:
=180-117
=63
M<G:
=180-63
=117
Solve the following formula for t.
Q=F+ Frt
(Simplify your answer.)
20 poäng One positive number is 5 more than another. The sum of their squares is 53. What is the larger number?
One positive number is 5 more than another. The sum of their squares is 53. Then the larger number is 8.
Lets take x be the smaller number, then x + 5 = the larger number. Thus, we have the equation:
x2 + (x + 5)2 = 53
By Simplifying the equation, we get: 2x2 + 10x + 25 = 53
By Solving this quadratic equation, we get x = 3 and the larger number is 8.
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
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The area of this circle is 72π m².
What is the area of a 45º sector of this circle?
Responses
8π m²
9π m²
12π m²
18π m²
The area of the sector is evaluated to be equal to 9π square meters
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
For the area of circle 72π m²;
πr² = 72π m²
r² = 72 m²
hence the area of the sector is calculated as follows:
area of the sector = (45°/360°) × π × 72 m²
we simplify by multiplication and division
area of the sector = 1/8 × π × 72 m²
area of the sector = π × 9 m²
area of the sector = 9π m².
Therefore, the area of the sector is evaluated to be equal to 9π square meters
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Please Show detailed algebraic work.
Using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
Given,
The initial amount of caffeine in the beverage = 120 mg
The rate at which the caffeine decreases = 12% per hour w
We are asked to find the time taken for the caffeine amount to become 10mg.
Now let the initial amount be 100 per cent.
After one hour, the amount becomes (100-12) = 88% of 120 = 0.88 * 120
So after every one hour, there is 88% caffeine left.
Now after two hours,
the amount of caffeine = 88% of (0.88*120) = 0.88*0.88*120 = 120(0.88)²
So after x hours, we can write the equation as:
Amount of caffeine left C(x) = 120(0.88)ˣ
Now for 10mg to be left, the time taken is:
10 = 120(0.88)ˣ
1/12 = (0.88)ˣ
log (1/12) = x log(0.88)
-1.079 = x (-0.056)
x = 19.27 hours
Therefore using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.
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You are flipping two coins. Find the probability of flipping two tails.
A. 1/2
B. 1/24
C. 1/8
D. 1/4
Answer:
D. 1/4
Step-by-step explanation:
The probability of flipping a tail is 1/2. To find the probability of flipping two tails, multiply.
1/2 x 1/2 = 1/4
Answer: Here we will learn how to find the probability of tossing two coins.
Let us take the experiment of tossing two coins simultaneously:
When we toss two coins simultaneously then the possible of outcomes are: (two heads) or (one head and one tail) or (two tails) i.e., in short (H, H) or (H, T) or (T, T) respectively; where H is denoted for head and T is denoted for tail.
Therefore, total numbers of outcome are 22 = 4
The above explanation will help us to solve the problems on finding the probability of tossing two coins.
Step-by-step explanation:
THE ANSWER MUST BE AT LEAST 1/4 OR 1/8
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