If the baseball diamond at a playground is a square with sides that measure 80 feet. About how long would a straight line be from home plate to second base is: B.113.1 feet.
Determining the distanceGiven data
Sides measure in feet = 80 feet.
Since the diagonal tend to forms the hypotenuse of a right triangle with both sides of 80 feet
Hence,
Using the Pythagoreans theorem to determine the distance
(80)² + (80)² = x²
6400 + 6400 = x²
x² = 12,800
x = √ 12,800
x = 113.1 feet
Therefore the correct option is B.
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4.7.4 Modeling Pumpkin launch, we were covering graphs of quadratic functions please help! Thank you
Using a quadratic function, it is found that:
a) The coordinates of the second x-intercept are: (50,0).
b) The vertex shows the maximum flight of the projectile.
c) The coordinates of the vertex are (25, 62).
3) The graph of the equation y = -0.0992(x² - 50x) is given at the end of the answer.
Quadratic functionA quadratic function has two x-intercepts, x' and x'', and is defined as follows:
y = a(x - x')(x - x'').
The intercepts are given as follows:
First x-intercept: coordinates (0,0), as the fruit is thrown from the ground.Second x-intercept: coordinates (50,0), as the fruit travels a distance of 50 feet to hit the ground.The vertex is found as follows:
x-coordinate of 25, which is the mean of the two intercepts.y-coordinate of 62, which is the maximum height.Hence the coordinates are: (25, 62).
The equation can be defined as follows:
y = ax(x - 50)
y = a(x² - 50x).
When x = 25, y = 62, hence the leading coefficient is found as follows:
62 = a(25² - 50(25))
-625a = 62
a = -62/625
a = -0.0992.
Hence the equation is:
y = -0.0992(x² - 50x).
The domain of the function is between the roots, hence 0 ≤ x ≤ 50, and the graph is sketched at the end of the answer.
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in 1982, the us mint changed the composition of pennies from all copper to zinc with copper coating. pennies made prior to 1982 weigh 3.1 grams. pennies made since 1982 weight 2.5 grams. if you have a bag of 1267 pennies, and the bag weighs 3541.9 grams, how many pennies from each time period are there in the bag?
Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams. 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
Given that,
The 1982 change in pennies composition from all copper to zinc with copper coating was made by the US Mint. Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams.
We have to find how many coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
An issue of quantity and amount. In this context, the term "amount" refers to weight. The variables should be identified with letters that will make them easy to distinguish: Z for largely zinc and C for all copper. Create weight and quantity equations:
C + Z = 1287
3.1 C + 2.5 Z = 3601.5
By multiplying all three components of the first equation by -2.5 and placing them under the second equation, drawing a line, and then subtracting, you can eliminate the Z using this method.
3.1 C + 2.5 Z = 3601.5
-2.5 C - 2.5 Z = -3217.5
--------------------------------
0.6 C = 384
Divide both sides by .6.
C = 640
Subtract 640 from 1287.
Z = 647
Therefore, 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
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y = 2x - 4 what is the slope
Remember that the slope-intercept equation of the line is:
[tex]y=mx+b[/tex]where 'm' is the slope and b is the y-intercept.
In this case, we have the following:
[tex]y=2x-4[/tex]therefore,, the slope is m = 2
Whileat the fruit stand, ramon bought 3 punds of apples that cost $0.89 per pound and 4 cantaloupes that each cost $1.09. about how much money did he spend, not including tax?
The total money spent on fruits is $7.03
While at the fruit stand, Ramon bought the following fruits,
3 pounds of apples that cost $0.89 per pound
4 cantaloupes that each cost $1.09
So, the total amount he spent on the materials he bought without including taxes is,
Total money spent = 3 x ( 0.89 ) + 4 x ( 1.09 )
= 2.67 + 4.36
= 7.03
The total money spent on fruits is $7.03
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this is a super hard one
Notice that in the given sequence the difference between the first two terms is 7 so the solution must be in terms of multiples of 7 plus a constant. The only two options that have this characteristic are first and last ones, for the sum to consider the first term the sum must start for r=0.
Answer: last option.
RS =9y + 2, ST = 2y + 3, and RT = 60
Answer:
y=5
Step-by-step explanation:
RS + ST = RT
9y+2 + 2y+3 = 60
11y + 5 = 60
11y = 55
Y = 5
if a baker has 7/3 cups of chocolate, the baker can make a maximum of .... cakes.
She calls for 4/5 cup of chocolate
She had 7/3 cups of chocolate.
[tex]\begin{gathered} \text{The bake can make a ma}\xi mum\text{ of = }\frac{7}{3}\text{ }\frac{.}{.}\text{ }\frac{4}{5} \\ \text{ = }\frac{7}{3}\text{ x }\frac{5}{4} \\ \text{ = }\frac{35}{12} \\ \text{ = 2}\frac{11}{12} \\ \end{gathered}[/tex]Maximum number of cakes a baker can make = 2
4x > 28 solve the inequality for x and simplify your answer as much as possible
Answer:
x > 7
Step-by-step explanation:
x = 28 ÷ 4
x > 7
that's it
Hey there!
4x > 28
DIVIDE 4 to BOTH SIDES
4x/4 > 28/4
SIMPLIFY it
x > 28/4
x > 7
It is an open circle started at 7 & it’s going to the left of the number line
Therefore, your answer should be:
x > 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
7. Solve by using extracting square roots 4a²-25= 0
pa answer po rn
w solution po
[tex]4a^{2} -25=0\\(2a-5)(2a+5)=0\\2a-5=0 \\or 2a+5=0\\\\a=\frac{5}{2} \\\\or\\\\a=-\frac{5}{2}[/tex]
IF YOU CHECK CAREFULLY YOU WILL FIND THAT THIS EQAUTION IS MADE OF DIFFERENCE OF SQUARES.
GOODLUCK!!
Evaluate the function for the following values:
f(1) =
f(2)=
f(3) =
Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]
Step-by-step explanation:
[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]
what is 11/12 ÷ 1/30 2 1/40 2 3/40 3 1/30 3 2/3
The given expression is
[tex]\frac{11}{12}\colon\frac{1}{3}[/tex]First, we change 1/3 for its reciprocal to transform the division into a product.
[tex]\frac{11}{12}\cdot\frac{3}{1}[/tex]Then, we multiply the fractions.
[tex]\frac{11\cdot3}{12\cdot1}=\frac{33}{12}=\frac{11}{4}[/tex]At last, we transform the fraction into a mixed fraction.
[tex]\frac{11}{4}=2\frac{3}{4}[/tex]Therefore, the right answer is B. 2 3/4.Please help me do my Math Homework ASAP, it is attached.
Answer:
Step-by-step explanation:
an article suggests that a poisson process can be used to represent the occurrence of structural loads over time. suppose the mean time between occurrences of loads is 0.4 year. (a) how many loads can be expected to occur during a 4-year period? loads (b) what is the probability that more than twelve loads occur during a 4-year period? (round your answer to three decimal places.) (c) how long must a time period be so that the probability of no loads occurring during that period is at most 0.3? (round your answer to four decimal places.) yr
The probability of no loads occurring during that period is at most 0.3 exists 3.2 years.
How long must a time period be so that the probability of no loads occurring during that period?Given: Mean time between occurrence = 0.4 year
A number of loads expected to occur during a 4 year period
Period = 4
Mean time = 0.4
Let the formula = Period/Mean Time
The number of loads expected to occur during a 4-year period
= 4/0.4 = 10 loads
B. Probability that more than 11 loads occur during 4 year period
The expected number of loads during 4-year period = 10 (from A above)
mean = 10
Using Poisson distribution,
P(k events in interval)= (λ^k * e^-k)/k!
where: k = 0, 1, 2,3,4, . . ., 11 and λ = 10.
P(k = 0) = (1[tex]0^0[/tex] × [tex]e^{-10[/tex])/0! = 0.000045
P(k = 1) = (1[tex]0^1[/tex] × [tex]e^{-10[/tex])/1! = 0.000454
P(k = 2) = (10² × [tex]e^{-10[/tex])/2! = 0.00227
P(k = 3) = (10³ × [tex]e^{-10[/tex])/3! = 0.007567
P(k = 4) = (1[tex]0^4[/tex] × [tex]e^{-10[/tex])/4! = 0.018917
P(k = 5) = (1[tex]0^5[/tex] × [tex]e^{-10[/tex])/5! = 0.037833
P(k = 6) = (1[tex]0^6[/tex] × [tex]e^{-10[/tex])/6! = 0.063055
P(k = 7) = (1[tex]0^7[/tex] × [tex]e^{-10[/tex])/7! = 0.090079
P(k = 8) = (1[tex]0^8[/tex] × [tex]e^{-10[/tex])/8! = 0.112599
P(k = 9) = (1[tex]0^9[/tex] × [tex]e^{-10[/tex])/9! = 0.12511
P(k = 10) = (1[tex]0^{10[/tex] × [tex]e^{-10[/tex])/10! = 0.12511
P(k = 11) = (1[tex]0^{11[/tex] × [tex]e^{-10[/tex])/11! = 0.113736
The probability that more than 11 loads occur during a 4-year period is then given by the following Express
1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]
substitute the values in the above equation, we get
= 1 - [0.000045 + 0.000454 + 0.00227 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.12511+ 0.12511 + 0.113736]
simplifying the equation, we get
= 1 - 0.571665 = 0.428335
C. How long must a time period be so that the probability of no loads occurring during that period is at most 0.3
(λ^0 * e^-λ)/0! = 0.3
⇒ e^-λ/1 = 0.3
simplifying the above equation, we get
⇒ e^-λ = 0.3
⇒ -λ = ln 0.3
⇒ -λ = -1.204
⇒ λ = 1.204
The time period = 4 years / 1.204
Time period = 3.2 years
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There are 60 members in the school glee club. The glee club needs to raise at least $5,000 for a trip toa national competition. The school agreed to contribute $1,000 toward the trip. Which of theinequalities below shows the amount of money that each glee club member needs to raise to help payfor the trip.a) 60x + 1,000 > 5,000b) 60x + 5,000 > 1,000c) 1,000x + 60 < 5,000
Let x be the amount raised by each club member. Since there are 60 members, the amount raised by them would be
[tex]60x[/tex]Now, we know the school contributed $1,000. Now, the amount raised is:
[tex]60x+1000[/tex]Since this amount has to be at least $5,000, we have that the inequality that shows the amount of money that each glee club member needs to raise to help pay for the trip is:
[tex]60x+1000>5000[/tex]Answer: Option A
Andrew earns 30% on all sales plus a retainer of £125 per week.
If he earns £893 in one week, find the value of his sales for that week.
If Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.
The total amount he earned = $893
The amount of retainer he earned = $125
The percentage he earned = 30%
30% of the sales = The total amount he earned - The amount of retainer he earned
Substitute the values in the equation
= 893-125
= $768
Consider the total sales as x
Then,
x × (30/100) = 768
0.3x = 768
x = 768/0.3
x = $2560
Hence, if Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.
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Write the equation of the line passing through (-3,1) that is perpendicular to 3x-8y=16
two lines are perpendicular when their slope is inverted and have the opposite sign
the general form of the equation line is-3,1
[tex]y=mx+b[/tex]where m is the slope
rewrite
[tex]\begin{gathered} 3x-8y=16 \\ 3x-16=8y \\ y=\frac{3x-16}{8} \\ y=\frac{3}{8}x-2 \end{gathered}[/tex]so, the slope 3/8
the slope of the other line is
[tex]\frac{3}{8}\longrightarrow-\frac{8}{3}[/tex]to write the new equation of the line we use the slope and replace the point (-3,1)
[tex]\begin{gathered} (1)=(-\frac{8}{3})(-3)+b \\ 1=8+b \\ b=-7 \end{gathered}[/tex]now, replace b and the slope to create the line
[tex]y=-\frac{8}{3}x-7[/tex]fine the value of x. please help
Answer:
141 degrees
Step-by-step explanation:
The total angle interior of a triangle is 180 degrees. And the 2 angles opposite of x equal it so x=103+38
If f(x) = 5x, what is f¹(x)?
O f¹(x) = -5x
○ f¹(x) = -1/2 x
0 r²(x) = ²/1 x
O f¹(x) = 5x
The value of f¹(x) = x/5
What is function?
A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.
We are given f(x) = 5x
and we are to find inverse of f(x).
Replace f(x) by y.
So,
y = 5x
Isolate x
x = y/5
Replace x by f'(y)
So,
f'(y) = y/5
Replace all occurrences of y by x.
So,
f'(x) = x/5
Therefore, the inverse of function f(x) = 5x is f'(x) = x/5
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Whats the midpoint of line segment (-1,6), (3,0)
Answer:
(1,3)
Step-by-step explanation:
You can use the distance formula to help you solve the answer
Answer:
(1; 3)
Step-by-step explanation:
x = (-1 + 3)/2 = 1
y = (6 + 0)/2 = 3
21. What are the modes of the following sets of numbers?
a. 3, 13, 6, 8, 10, 5, 6
b. 12, 0, 15, 15, 13, 19, 16, 13, 16, 16
Answer:
6 and 16
Step-by-step explanation:
→ Find the most recurring number in sequence A
6
→ Find the most recurring number in sequence B
16
Eli dug a trench
18
20
of a meter long. The next day he dug another 17
20
B
of a meter. What is a reasonable estimate of the total length of the trench?
The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.
There could be only two terms, but there could be one hundred, a thousand, or a million.
Here are always an integer number of terms in a summation.
As per the given,
Length of the trench on the first day = 18/20 meters
Length of the trench on the second day = 9/20
Total length of the trench = 18/20 + 9/20
Take LCM as 20
⇒ (18 + 9)/20 = 27/20
⇒ 1.35 which is closest among the given option by 1 1/2 meters.
Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".
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a=3,k=12,z=6,h=4 Evaluate the algebraic expression z+15=?
since z=6, so z+15 is equal to 21
or a+k+z=21
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
c = 23
Step-by-step explanation:
To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.
(2c + 51)° = 97°
Next, you want to subtract 51 from both sides.
(2c + 51) - 51 = 97 - 51
2c = 46
Lastly, you isolate c by dividing 46 by 2.
c = 46 ÷ 2
c = 23
4. 3. The price of a computer is $699.00. The sales tax rate is 8%. What is the 10 points
sales tax on this computer in dollars and cents?
Mark only one oval.
0000
$55.92
$754.92
$5,592.00
$5.59
Answer:
$754.92
Step-by-step explanation:
699.00 plus 8% of 699.00 is 754.92
Went to start the sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 is Gwen correct explain why or why not
The sum of -1 (3/4) and 2 (1/2) is the same as the difference between 2 (1/2) and 1 (3/4).
Firstly, we will convert the mixed fractions into improper fractions.
-1 and 3/4 = -7/4
2 and 1/2 = 5/2
Addition of -1 (3/4) and 2 (1/2) = -7/4 + 5/2 = -7/4 + 10/4 = 3/4
Difference between 2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4
As both the values equal to 3/4 , we can say that the addition of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
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convert improper fractions to mixed number 7/5
The mixed fraction of the given improper fraction is [tex]1\frac{2}{5}[/tex].
According to the question,
We have the following improper fraction:
7/5
Now, to convert this into mixed fraction we will divide the numerator by the denominator and add the quotient before the fraction and the remainder will form the numerator and the denominator will remain same as that of this improper fraction.
(More to know: there are three kinds of fraction: proper fraction (in proper fraction, we have denominator larger than numerator), improper fraction and mixed fraction.
So, we will divide 7 by 5:
[tex]1\frac{2}{5}[/tex]
Hence, the mixed fraction of 7/5 is [tex]1\frac{2}{5}[/tex].
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What is the lowest common multiple of 19 & 9
Solution:
LCM of 9 and 19 is the smallest number among all common multiples of 9 and 19.
The first few multiples of 9 and 19 are (9, 18, 27, 36, 45, 54, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively.
There are 3 commonly used methods to find LCM of 9 and 19 - by listing multiples, by division method, and by prime factorization.
To calculate the LCM of 9 and 19 by the division method, we will divide the numbers(9, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 19.
In this case, we get:
Then, the LCM would be:
[tex]3\text{ x 3 x 19 = }171[/tex]so that, the correct answer is:
[tex]171[/tex]17. What are the roots of the equation s² - 7 = 74?
18. One of the roots of x² - 8x = 0 is 8. What is the other root?
paanswer po ngaun
w solution if meron po sana
Answer:
17. s = 9
18. x = 8x^(½)
Step-by-step explanation:
s² - 7 = 74?
s² = 74 + 7
s² = 81
√(s²) = √(81)
s = 9
x² - 8x = 0
x² = 0 + 8x
x² = 8x
√(x²) = √(8x)
x = 8x^(½)
OR by factoring
x²−8x=0
x(x−8)=0
x=0 or x−8=0
x=0 or x=8
The carpenter cuts 1-
1
inches off a piece of wood every 2 minutes. How many inches
2
will be cut in 25 min?
7+3(p-1)=64 how to solve
Answer:
p = 20
Step-by-step explanation:
7 + 3(p - 1) = 64 ( subtract 7 from both sides )
3(p - 1) = 57 ( divide both sides by 3 )
p - 1 = 19 ( add 1 to both sides )
p = 20
