The total weight of the metal bar is 45.002 grams.
Given:
While mining, Peter found a large metal bar that contained 33 grams of gold.
Peter also determined that the bar was 73.33% gold.
73.33% = 33 grams
divide by 73.33 on both sides
73.33%/73.33 = 33/73.33 grams
1% = 0.45002 grams
Multiply on 100 on both sides
1%*100 = 0.45002*100
100% = 45.002 grams.
Therefore the total weight of the metal bar is 45.002 grams.
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Find the square root that is a real number
The square root of √-36 is 0.
What is square root?A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol "sqrt"—square root of, end square root. The opposite of squaring an integer is finding its square root. In mathematics, a square root is a factor that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.So, √-36:
Calculate the square root as follows:
Therefore, the square root of √-36 is 0.
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57) A roundabout consists of a carriageway with a width of 4.5 meters and a circular inner area with a diameter of 16 meters.
a) There is a fence around the inner area. How many meters is the length of the fence? Round to two decimal places.
b) The inner area is sown with grass. 25 grams of grass seed is needed per m². Calculate how many kg of grass seed is needed for the indoor area. Round to one decimal place.
c) Calculate the area of the carriageway on the roundabout in m². Round to one decimal place.
d) In the case of road works, a white line will be placed in the middle of the carriageway of the roundabout. The striping car travels at a speed of 25 cm per second. How many minutes does it take to apply the line? Round to wholes.
a) Length of Fence = 50 meters
b) Weight of Grass Seeds = 20 kg
c) Area of Carriageway = 516 sq. meters
d) Time taken by the Striping Car = 7.6 minutes
What is a Circle?
A circular plane figure with a circumference made up of points equidistant from a given point (the center).
Solution:
a) To calculate the length of fence we need to find the circumference of the inner circle
Circumference of Circle = 2*22/7 *Radius
Circumference of Circle = 2 * 22/7 * (16)/2
Circumference of Circle = 50.24
So, the length of fence is 50 meters approx
b) To calculate the the total weight of grass we need to first find the area of the inner circle
Area of Circle = 22/7 * (Radius)^2
Area of Circle = 22/7 * (16)^2
Area of Circle = 22/7 * 256
Area of Circle = 803.84 meter sq.
For 1 meter sq. = 25 grms of grass seeeds are required
So, for 804 meters = 25*804 = 20100 grams
20100 grams = 20.1 kg = 20 kg (approx)
c) The are of Inner Carriageway will be calculated by substracting the area of inner circle from outer circle
Area of Outer Circle = 3.14 * (16+4.5)^2
Area of Outer Circle = 1320 sq. meters (approx)
Area of Inner Circle = 804 sq. meters (approx) #we have calculated it above
Area of Carriageway = 1320 - 804 = 516 sq. meters (approx)
d) Speed of Stripping Car = 25 cm/sec
Circumference of the part to be stripped = 2*3.14*(16+2.25)
Circumference = 115 meters approx. = 11500 cm
Time = Distance / Speed
Time = 11500/25 = 460 seconds
460 seconds in minutes = 7.6 minutes
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C: Determine the average rate of change between day 2 and day 4. Show your work. (4 points)
A) It is an exponential equation.
B) y = 2^x
C) The rate between days 2 and 4 is 6 minutes per station number.
Is the data modeling a linear or an exponential equation?Here we have the following data:
(1, 2), (2, 4), (3, 8), (4, 16)
What you can see is that the x-value of the points increases equially between consecutive pairs (increases of one unit).
while the y-value does not do that.
First, it increases by 2, then by 4, then by 8.
So this is an exponential relation.
B) A general exponential will be of the form:
y = a*(b)^x
Usin the first two pairs (1, 2) and (2, 4) we can write two equations:
2 = a*b^1 = a*b
4 = a*b^2
So we have a little system of equations:
2 = a*b
4 = a*b*b
If we take the second equation and we divide that by the first one we get:
4/2 = (a*b*b)/(a*b)
2 = b
Replacing that in the first equation we get:
2 = a*2
2/2 = a = 1
The equation is:
y = 2^x
C) The average rate of change will be:
R = (2^4 - 2^2)/(4 - 2) = (16 - 4)/2 = 12/2 = 6
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A) It is an exponential equation.
B) y = 2^x
C) The rate between days 2 and 4 is 6 minutes per station number.
4.
The sum of two odd consecutive integers is 88. Find the integers.
Answer:
43 and 45
Step-by-step explanation:
→ State an expression for 2 odd consecutive numbers
2x + 1 and 2x + 3
→ Find the sum
4x + 4
→ Equate to 88
4x + 4 = 88
→ Minus 4 from both sides
4x = 84
→ Divide both sides by 4
x = 21
→ Substitute into original expressions
43 and 45
Levine Labs used 50,000 ounces of specimen adhesive during the year. The direct materials standard allows 1.50 ounces of adhesive at a price of $0.40 per ounce for each pathology test. The direct materials quantity variance was $880 Favorable.
How many pathology tests did Levine Labs complete during the year?
(Round per unit value to 2 decimal places, e.g. 15.25 and final answer to O decimal places, e.g. 125.)
Pathology tests ____?
The number of pathology tests that were completed during the year by Levine Labs are 34,800 tests.
What is the calculation showing the above answer?Note that Material quantity variation - Material quantity variation describes the cost difference caused by variations in the actual material used and the standard material to be utilized.
Material quantity Variance =
(Actual material used- Standard material used) x Standard cost
(50000-no of test x 1.5) x 0.4 = -880
-2200 = 50000-(No of test*1.5)
No of test x 1.5 = 52,200
No of test = 52,200/1.5
No of test = 34,800
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Listed are 29 ages for Academy Award winning best actors in order from smallest to largest.
18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57;
58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 * *
Calculate the 20th percentile and the 55th percentile.
Answer:
Step-by-step explanation:
whats the difference between first, second degree murder
You buy 3 gallons of milk at $2.48/gallon, 2 gallons of
ice cream at $1.49/gallon, and 4 lbs of strawberries at
$0.58/1b. What is your total cost?
(1 point)
O$9.51
O$12.74
0$4.55
O$10.67
The total cost is $12.74
In this question, we have been given the cost of 1 gallon of milk, 1 gallon of ice-cream and 1 1b of strawberry.
1 gallon of milk costs $2.48,
1 gallon of ice-cream costs $1.49
and 1b of strawberry costs $0.58
You buy 3 gallons of milk, 2 gallons of ice cream, and 4 lbs of strawberries.
So by unitary method total cost would be,
(3 * 2.48) + (2 * 1.49) + (4 * 0.58) = $12.74
Therefore, the total cost is $12.74
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What is the answer for 6:3(3+3)
Answer:
the answer according to my solution is 06
use the given information about the polynomial graph to write the equation
Degree 5. Roots of multiplicity 2 at x = −3 and x = 2 and a root of multiplicity 1 at x = −2. y-intercept at (x, y) = (0,62).
For the given roots and point, the polynomial is:
p(x) = (62/72)*(x + 3)²*(x - 2)²*(x + 2)
How to write the polynomial?We know that a polynomial with leading coefficient a and the roots:
x₁, x₂, ..., xₙ
Can be written as:
p(x) = a*(x - x₁)*...*(x - xₙ)
Here we have the roots:
-3, -3, 2, 2, -2
Then we can write:
p(x) = a*(x + 3)*(x + 3)*(x - 2)*(x - 2)*(x + 2)
p(x) = a*(x + 3)²*(x - 2)²*(x + 2)
Now we also know that our polynomial passes through (0, 62), then:
p(0) = 62 = a*(0 + 3)²*( 0 -2)²*(0 + 2)
62 = a*9*4*2
62/(9*4*2) = a
62/72
then the polynomial is:
p(x) = (62/72)*(x + 3)²*(x - 2)²*(x + 2)
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Line b passes through the point (4, 2) and is
perpendicular
to the x-axis. What is the slope of line b?
Answer:
The slope would be undefined
Step-by-step explanation:
If the slope is perpendicular to the x-axis that means it is vertical, all vertical lines have undefined slopes therefore the slope is undefined.
A company issues 9%, 4-year bonds with a par value of $160,000 on January 1 at a price of $165,386, when the market rate of interest was 8%. The bonds pay interest semiannually. The amount of each semiannual interest payment is:
The amount of each semiannual interest payment is $7200.
Given that,
A company issues 9%, 4-year bonds with a par value of $160,000 on January 1 at a price of $165,386, when the market rate of interest was 8%. The bonds pay interest semiannually.
Simple interest is defined as the percentage of earnings on the lending for a period of time
Here,
Value of a single bond = $160,000
Issue price of bond = $165, 386
Rate of interest = 9%
the market rate of interest = 8%
Interest payment = Semi-annually
Semi-annual interest payment = Value of the single bond × rate of interest/2
= $160,000 × 0.09/2
= $7200
Thus, the amount of each semiannual interest payment is $7200.
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Give the answer and an explanation
A triangle is said to be right angle if one of the angles is 90 degrees, the value of the side x for the given right angle triangle is 50.51.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° .
The given right-angle triangle has the following sides,
AC = Base
BC = Perpendicular
AB = Hyp.
By tan function,
Since,tanθ = Perp/Base
tan29° = 28/x
x = 50.51
Hence, "A triangle is said to be right angle if one of the angles is 90 degrees, the value of the side x for the given right angle triangle is 50.51".
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=
Simple interest is given by the formula A P+Prt. Where A is the balance of the
account after t years, and P is the starting principal invested at an annual percentage rate
of r, expressed as a decimal.
Bill is investing $26,000 into a savings account that pays 2.6% simple interest. How long will
it take for this investment to double in value?
It will take
Round your answer to the nearest tenth.
years for this investment to double in value.
The investment will take 38.5 years to double in value.
What is simple interest?
The principal of a loan or the first deposit into a savings account serves as the basis for simple interest. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
P=$26,000 r=2.6%=0.026
A=2P=2(26,000)=$52,000
A=P+Prt
Substitute the known values
52,000=26,000+(26,000×0.026t)
52,000-26,000=676t
On simplifying, we get t= 38.46 years
Rounded number to the nearest tenth=38.5 years
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Question 6
A road drops 795 feet for every 265 feet forward, determine the slope of the road. The
slope can be positive or negative.
The slope of the road is 159/53
What is a slope?
How steeply a line slopes from left to right is known as its slope. By dividing a line's rise, or vertical change, by run, or horizontal change, one can calculate a line's slope, the slope of a line is always constant (it never varies).
To calculate the slope of a line using the formula
m = rise / run = (y₂ - y₁)/(x₂ - x₁)
where, m = slope
(x₁, y₁) = coordinates of the first point in the line
(x₂, y₂) = coordinates of the second point in the line
Here, we have
rise = 795
run = 265
by using the slope formula,
m = rise/run
m = 795/265
m = 159/53
Hence, the slope of the road is 159/53.
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how many craft sticks will be left over if 9 friends equally share a package of 85 craft sticks
Answer:
4 craft sticks
Step-by-step explanation:
Assuming that none of the craft sticks can be split in order to equally share the whole package, then the most craft sticks each person could have would be 9 because 9*9=81. This means that there would be 4 craft sticks left over because 85-81=4
Find function which gives the slope of the line tangent to j(x).
j(x)=4x55−x4+x2
A. 3x4−12x3+2x
B. 16x3−12x2+2
C. 4x4−4x3+2x
D. 4x4−4x3+2
Please help me thank you so much!
Answer:
please write it more clearly or take a pic
A teacher runs each morning before school. Last week, he ran a total of 5 3/4 miles. This week, he ran 4/5 of the total number of miles he ran last week. What is the total number of miles that the teacher ran last week and this week?
The total number of miles that the teacher ran both last week and this week was 10.35 miles
How to find the total number of miles?Last week, the teacher ran a total of 5 3/4 miles. For easier calculation, convert this to a decimal:
= 5 + 3/4
= 5 + 3 ÷ 4
= 5 + 0.75
= 5.75 miles
This week, the teacher ran 4 / 5 of the miles he ran the previous week:
= 5. 75 x 4/5
= 4.6 miles
The total number of miles the teacher ran both last week and this week were:
= 5.75 + 4.6
= 10.35 miles
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Answer:
10 7/20 miles
Step-by-step explanation:
332x39 how do you work it out
A sample of 39 customers was taken at a local computer store. The customers were asked the prices of the computers they had bought. The data are
summarized in the following table.
Number of computers Price (in dollars)
13 - 2300
11 - 1800
15 - 2150
Find the mean price for this sample. Round your answer to the nearest dollar.
The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
What is mean?A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilizes the sum of the series' values, and the geometric mean method, which uses the average of a group of products. However, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.acc to our question-
Mean price = total amount spent on computers / number of computers= (6*900 +18*800+14*2600+5*1750)/(6+18+14+5) =64,950/43 = 1510.47x f fx900 6 5400800 18 144002600 14 364001750 5 875043 64950xbar = Σxf/Σf = 64,950/43 = 1510.47hence,The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
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helppppppppppppppppppppp
Answer:
1) find the point on the function where it crosses the x-axis
2) find the set of values where x = 0
3) set x = 0 and solve for y; then put the two values into a coordinate pair
a car travels at an average speed of 52 miles per hour how long does it take to travel 273 milez
Answer:
5 hours 15 minutes
Step-by-step explanation:
using the relationship
time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{273}{52}[/tex] = 5.25 hours = 5 hours 15 minutes
Given the following function, the values of p and q are...
f(x)= 3x^2-x-4
A. p=1, q=3
B. p=4, q=3
C. p= -4, q= 3
D. p=3, q=-4
its in the picture♡
Answer:A. (10 x 3) + 8
Answer:
A : ( 10 * 3 ) + 8
Hope this helps!
Step-by-step explanation:
10 friends, each donate 3 pieces of clothing, ( 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 ) or ( 10 * 3 ), plus the 8 pieces of clothing Emily is donating. ( 10 * 3 ) + 8.
How many three-letter "words" can be made from 10 letters "FGHIJKLMNO" if repetition of letters (a) is allowed? Your answer is (b) is not allowed? Your answer is
a. The number of permutations of three letter words that can be formed with repetition is 1000 words
b. The number of permutations of three letter words that can be formed without repetiton is 720 words
What are permutations?Permutations are the number of ways in which x objects can be arranged out of n objects.
The number of permutations is given by ⁿPₓ = n(n - 1)(n -2)...(n - x + 1)
a. How to find the number of ways in which the 10 letters can be arranged if repetition is allowed?Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" with repetition, we note that there are 10 letters.
Since repetition is allowed, for the first slot, we have 10 letters, for the second position, we have 10 letters and for the third position, we have 10 letters.
So, the total number of permutations is n = 10 × 10 × 10
= 1000 words
So, the number of three letter words that can be formed is 1000 words
b. How to find the number of ways in which the 10 letters can be arranged if repetition is not allowed?Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" without repetition, we note that there are 10 letters.
Since repetition is not allowed, for the first slot, we have 10 letters, for the second position, we have 9 letters and for the third position, we have 8 letters.
So, the total number of permutations is ¹⁰P₃ = 10 × 9 × 8
= 720 words
So, the number of three letter words that can be formed is 720 words
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Solve each equation for x. Show all steps.
A) log base 4 (x^2 -12x+48) =2
B) 27^(4x-6) =(1/9)^(2x-7)
A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8
B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2
Solving equations: Determining the value of xFrom the question, we are to solve the given equations
The given equation is log₄(x² - 12x + 48) = 2
From one of the laws of logarithm, we have that
logₐ x = n ⇒ x = aⁿ
Thus,
log₄(x² - 12x + 48) = 2 becomes
(x² - 12x + 48) = 4²
x² - 12x + 48 = 16
x² - 12x + 48 - 16 = 0
x² - 12x + 32 = 0
Solve the quadratic equation
x² - 12x + 32 = 0
x² - 8x - 4x + 32 = 0
x(x - 8) -4(x - 8) = 0
(x - 4)(x - 8) = 0
x - 4 = 0 OR x - 8 = 0
x = 4 OR x = 8
B) 27^(4x-6) =(1/9)^(2x-7)
Solve for x
27^(4x-6) =(1/9)^(2x-7)
Express the bases in index form
3^3(4x-6) =(3)^-2(2x-7)
Equate the powers
3(4x - 6) = -2(2x - 7)
12x - 18 = -4x + 14
12x + 4x = 14 + 18
16x = 32
Divide both sides by 16
16x/16 = 32/16
x = 2
Hence, the value of x is 2
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We want 3 pizzas, each topped with 0, 1, 2, 3, 4, 5, or 6 of 6 available whole-pie toppings. How many different combinations of 3 such pizzas are possible if different pizzas need not have different toppings?
A letter is chosen at random from the word MATHEMATICS. Find the probability that it will be
a) an H
b) an M
c) a B
d) a vowel,
e) a letter other than an A
Answer:
a) 1/11
b) 2/11
c) 0/11
d) 4/11
e) 9/11
Step-by-step explanation:
'MATHEMATICS' has 11 letters.
a) there is only one H out of the 11 letters meaning the probability is 1/11
b) there are two M s out of the 11 letters meaning the probability is 2/11
c) there is no B in the word meaning the probability is 0/11
d) there are four vowels (2 A s, 1 E and 1 I) out of the 11 letters meaning the probability is 4/11
e) there two A s in the word and 11-2=9 meaning the probability is 9/11
Hope this helps :)
Bob’s bank charges him a $3.15 service fee every time he uses an out-of-network ATM. If Bob uses an out-of-network ATM an average of three times every two weeks, how much will he pay in service fees over the course of a year?
a.
$327.60
b.
$109.20
c.
$491.40
d.
$245.70
Please select the best answer from the choices provided
A
B
C
D
answer:
$245.70
why?:
1 year = 52 weeks
52/2= 26
26*3 = 78 times
78*3.15= 245.70
(-2,6), m = 4 !!!!!!!!!!!!
Answer:
y=4x+14
Step-by-step explanation:
Georgle is three times older than Maddle. If Georgle is 39 years old, which equation can be used to find m, Maddie's
age?
