Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)
Triangle XYZ is similar to triangle JKL.
triangle XYZ with side XY labeled 8.7, side YZ labeled 7.8, and side ZX labeled 8.2 and triangle JKL with side JK labeled 12.18
Determine the length of side LJ.
11.48
11.59
12.80
12.92
The correct answer among the choices provided is A. 11.48.
How to solveGiven that side XY of triangle XYZ corresponds to side JK of triangle JKL, we can set up the following proportion:
XY/JK = YZ/LJ
Substituting the given values:
8.7 / 12.18 = 7.8 / LJ
We solve this for LJ:
LJ = (7.8 * 12.18) / 8.7
Calculating that gives us:
LJ ≈ 11.48
So, the correct answer among the choices provided is A. 11.48.
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Diego is attending UTEP and has completed some courses worth 3 credits and some course worth 4 credits. he has earned a total of 59 credits after completing 18 courses. How many courses worth 4 credits has Diego completed
Answer:
3 credit course = 13
4 credit course = 5
Step-by-step explanation:
Given that :
Total credits = 59
Total courses = 18
Let :
Number of 3 credit course = x ; number of 4 credit course = y
x + y = 18 - - (1)
3x + 4y = 59 - - - (2)
x = 18 - y
3(18 - y) + 4y = 59
54 - 3y + 4y = 59
54 + y = 59
y = 59 - 54
y = 5
x = 18 - 5
x = 13
3 credit course = 13
4 credit course = 5
Answer:
The answer above me
Step-by-step explanation:
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
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Last math question please help thank you
Step-by-step explanation:
QR= 1.5 inches
TS= 2 inches
TP= 3.8 inches
RS= 1.4 inches
PQ= 2.6 inches
now complete ur promise
Answer:
Step-by-step explanation:
Remark
The question says to increase the lengths of each side by a factor of 1.5.
That means that every measurement we see on the diagram is multiplied by 1.5
QR = given length times 1.5
given length = 1.5
QR = 1.5 * 1.5
QR = 2.25
TS = given length * 1.5
TS = 2 * 1.5
TS = 3
TP = given length * 1.5
TP given = 3.8
TP = 3.8 * 1.5
TP = 5.7
RS = given length * 1.5
given length = 1.4
RS = 1.4 * 1.5
RS = 2,1
PQ = given length * 1.5
given length = 2.6
PQ = 2.6 * 1.5
PQ = 3.9
a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south carolina average? use
The hypotheses for \(H_{0}\) is \(\µ_{1}\) = \(\µ_{2}\) and for \(H_{1}\) \(\µ_{1} > \µ_{2}\) (claim)
Given:
Nationwide scores as n1=1000, \(x_{1}\)` = 21.4 ,σ1 = 3
Carolina scores as n2=500, \(x_{2}\)` = 21.2 ,σ2 = 3
So from here we can say
µ represents population mean.
\(u_{1}\) represent population mean for nationwide scores.
\(u_{2}\) represents population mean for Carolina scores.
\(H_{0}\) is \(\µ_{1}\) = \(\µ_{2}\) and for \(H_{1}\) \(\µ_{1} > \µ_{2}\) (claim)
Given Question is incomplete, Complete Question here,
a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south Carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south Carolina average?
use α=0.01 and \(\µ_{1}\) for the nationwide mean act score.
State the hypotheses and identify the claim.
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how to work out 1/4 of 24?
Answer:
6
Step-by-step explanation:
work out 25% of 24 then turn the answer into a fraction
Answer:
6 is the answer
Step-by-step explanation:
1/4 *24
1*6
6
find the 66th term in the following arithmetic sequence
-92, -85, -78, -71
Answer:
The 66th term is 363.
Step-by-step explanation:
Here,
a = -92 b = -85
d = b - a = -85 -(-92) = 7
n = 66
t66 = ?
We know,
tn = a+(n - 1)d
t66 = -92+(66 - 1)7
= 363
rk. .) If B is the midpoint of AC and AB=20, BC=2x, find x and the length of AC.
AB = BC
Since B is the midpoint of AC , Both segments AB and BC are equal:
Replacing with the values given:
20 = 2x
Solving for x
20/2 = x
10=x
Since:
AC= AB+BC
AC = 20+2x
Replacing x=10
AC = 20+2(10)
AC=20+20
AC=40
What is the area under the curve between z=-1 and z=2 standard normal distribution
The area under the curve between z = -1 and z = 2 in the standard normal distribution is approximately 0.8186.
The standard normal distribution, also known as the Z-distribution, is a probability distribution with a mean of 0 and a standard deviation of 1. The area under the curve represents the probability of a random variable falling within a certain range. To find the area under the curve between z = -1 and z = 2, we can use statistical tables or calculators that provide the cumulative distribution function (CDF) for the standard normal distribution. The CDF gives the probability that a random variable is less than or equal to a given value.
Using the standard normal distribution table or calculator, we find that the CDF value for z = -1 is approximately 0.1587 and the CDF value for z = 2 is approximately 0.9772. To find the area under the curve between these two z-values, we subtract the CDF value for z = -1 from the CDF value for z = 2: 0.9772 - 0.1587 = 0.8185. Therefore, the area under the curve between z = -1 and z = 2 in the standard normal distribution is approximately 0.8186. This represents the probability that a random variable from the standard normal distribution falls within the range of -1 to 2.
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How many numbers between 1 11 and 100 100100 (inclusive) are divisible by 3 33 or 10 1010?.
There are 99 numbers between 1,011 and 100,100 (inclusive) that are divisible by either 3, 33, or 10,1010.
To find the numbers between 1,011 and 100,100 that are divisible by either 3, 33, or 10,1010, we need to determine the count of numbers divisible by each of these three numbers within the given range.
For a number to be divisible by 3, the sum of its digits must be divisible by 3. Applying this rule to the given range, we observe that every third number starting from 1,011 (1,011, 1,014, 1,017, and so on) will be divisible by 3. Counting the numbers in this pattern gives us a total of 33 numbers divisible by 3 within the range.
Similarly, for a number to be divisible by 33, it must be divisible by both 3 and 11. Since we have already counted the numbers divisible by 3, we need to identify the numbers divisible by 11 within the range. By examining the range, we can see that there are nine numbers divisible by 11 (1,011, 1,022, 1,033, and so on). However, we need to exclude the numbers that are already counted in the previous category (divisible by 3), so we subtract three numbers (1,011, 1,044, and 1,077). This gives us a total of six additional numbers divisible by 33.
Finally, to find the numbers divisible by 10,1010, we need to check if any numbers within the range satisfy this condition. Since 10,1010 is a large number, it is unlikely that any numbers within the given range would be divisible by it.
Adding the numbers from both categories, we have 33 numbers divisible by 3 and six numbers divisible by 33, giving a total of 39 numbers. Therefore, there are 99 numbers between 1,011 and 100,100 (inclusive) that are divisible by either 3, 33, or 10,1010.
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LA Galaxy have won 36%of their soccer matches .If they have played 50 matches ,how many have they won ?
If LA Galaxy has won 36% of their soccer matches, this means that they have won 36/100 * 50 = 18 matches.
So, they have won 18 matches out of 50.
Step-by-step explanation:
percentage of soccer matches won = 36%
total matches = 50
matches won = 36/100 * 50
=18
A right triangle is shown, where the horizontal leg has a measure of 48 centimeters (cm), and the hypotenuse has a measure of 73 cm.
Answer:
55
Step-by-step explanation:
Using the Pythagorean theorm:
a^2+b^2=c^2
48^2+b^2=73^2
b^2=73^2-48^2
b^2=3025
b=55
Tell whether the ordered pair is a solution to the equation.
x=9;(9,6)
Answer:
yes, it is
Step-by-step explanation:
The value of x in the ordered pair (x, y) = (9, 6) is 9. That satisfies the equation ...
x = 9
Substituting 9 for x, we get a true statement:
9 = 9
Answer:
Step-by-step explanation:
25 points will mark brainliest
Answer:
i think x would be 0.8
sorry if im wrong :( its been awhile since ive done this stuff
Step-by-step explanation:
find the value of x
Step-by-step explanation:
The angle 67° is corresponding with the expression (4x+3°) and corresponding angles are equal
4x+3°=67°
4x=67°-3°
4x=64°(divide both sides by 4)
x=16
betermine if ABCD is a rhombus, rectangle, square or none
A(-6,-1) B(4,-6) C(2,5) D(-8,10)
Answer:
ABCD forms a rhombus
Step-by-step explanation:
When you graph it out on a graph, the points make a rhombus
Triangle OPQ is similar to triangle RST. Find the measure of side ST. Round your answer to the nearest tenth if necessary
Given that triangles OPQ and RST are similar triangles, the measure of side ST is: 75.3.
What are Similar Triangles?The ratio of the corresponding sides of two similar triangles are always equal, meaning the sides are proportional to each other.
Given:
OP = 17ST = 31PQ = 7Since Triangle OPQ is similar to triangle RST, therefore:
RS/OP = ST/PQ
Substitute
RS/17 = 31/7
Cross multiply
RS = (31 × 17)/7
RS = 75.3
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What is the quotient of 3.55 x 106 and 7.1 x 102 expressed in scientific notation?
PLEASE HELP THIS IS FOR A TEST
Answer:
\(5\times10^3\)
Step-by-step explanation:
\(3.55\times10^6 \div 7.1 \times 10^2\)
Exponents are positive:
\(3.5.5.0.0.0.0. = 3550000\)
\(7.1.0.=710\)
\(3550000 \div 710 = 5000\)
Convert back into scientific notation:
\(5000 = 5 \times 10^3\)
\(= 5 \times10^3\)
Hope this helps.
Answer: 5 x 10^3
Step-by-step explanation:
Fill in the blank. Someone who works 40 hours per week for 50 weeks per year, with two weeks off, would work around __________________hours per year.
Answer:
about 1920
step by step explanation:
40×50weeks=2000hours per year.
40×2weeks(the weeks off) = 80
2000-80= 1920hours per year
Simplify -8a(-6a) Show each step of your work.
i will mark you brainiest
Answer:
\(48a^{2}\)
Step-by-step explanation:
First, multiply the numbers
-8a ( -6)a
48aa
Next, We can combine the exponents
\(48a^{2}\)
That is all you need to do. : - )
A coin is loaded so that the probability of heads is 0.9 and the probability of tails is 0.1. Suppose that the coin is tossed twice and that the results of the tosses are independent. For i = 1 and 2, let H; be the event that the result of toss i is heads, and let T; be the event that the result of toss i is tails. (a) What is the probability (as a %) of obtaining exactly two heads? 81 % (b) What is the probability (as a %) of obtaining exactly one head? The probability of obtaining exactly one head is P((H, NT, U (H, NT,)) v U which equals %. Enter an exact number. (C) What is the probability (as a % of obtaining no heads? % (d) What is the probability of obtaining at least one head? % Use the binomial theorem to expand the expression.
a) The probability of obtaining exactly two heads is 81%.
(b) The probability of obtaining exactly one head is 18%.
(c) The probability of obtaining no heads is 1%.
(d) The probability of obtaining at least one head is 99%.
(a) The probability of obtaining exactly two heads can be calculated by multiplying the probabilities of getting heads on both tosses. Given that the probability of heads is 0.9, the probability of obtaining two heads is 0.9 * 0.9 = 0.81, or 81%.
(b) To calculate the probability of obtaining exactly one head, we need to consider two cases: (1) heads on the first toss and tails on the second toss, or (2) tails on the first toss and heads on the second toss. The probability of heads on the first toss is 0.9, and the probability of tails on the second toss is 0.1. Multiplying these probabilities gives 0.9 * 0.1 = 0.09. Similarly, the probability of tails on the first toss and heads on the second toss is 0.1 * 0.9 = 0.09. Adding these two probabilities together gives a total probability of 0.09 + 0.09 = 0.18, or 18%.
(c) The probability of obtaining no heads can be calculated by multiplying the probabilities of getting tails on both tosses. Given that the probability of tails is 0.1, the probability of obtaining no heads is 0.1 * 0.1 = 0.01, or 1%.
(d) The probability of obtaining at least one head can be calculated by subtracting the probability of obtaining no heads from 1. In this case, the probability of obtaining no heads is 0.01 (as calculated in part c). Therefore, the probability of obtaining at least one head is 1 - 0.01 = 0.99, or 99%.
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Danny is painting a doghouse to make it durable he will paint all sides including the bottom the dog house is shaped like a rectangular prism with a triangular prism on top as shown how many cans of paint does Danny need to cover the doghouse if each can covers 20ft squared
Answer:
15 cans
Step-by-step explanation:
There are two shapes that make up the dog house, they are the triangular and rectangular prism, with the combination of a semi-circle and rectangle as the door opening.
The area of a rectangle for the top ( T ) and bottom ( B ) side view:
top height = 3ft, and width= 8ft
bottom height = 4.5ft, width= 8 ft
Area ( T ) = 3 X 8 = 24 ft^2
Area ( B ) = 4.5 X 8 = 36ft^2
The front and back view is a triangle and rectangle:
area of triangle = 1/2 x base x height
with the base = 4ft, and sides= 3 ft
height = sqrt( side^2 - (1/2 height)^2 )^0.5
= sqrt( 9 - 4 ) = 2.235
area of triangle( front and back ) = 1/2( 4 x 2.235 ) = 4.47 ft^2
area of rectangle ( back ) = 4 x 4.5 = 18ft
The entrance is a rectangle with area = 2.5 x 2 = 5ft^2
and semi-circle with area = (πr^2)/2 = (3.14 x 1^2)/2 = 1.57ft^2
area of entrance = 5 + 1.57 = 6.57ft^2
area of front view = 18 - 6.57 = 11.43ft^2
the total area of the doghouse is = 11.43 + 18 + 72 + 48 + 8.94 = 158.37ft^2
this is for just the outside. to get the total for inside and outside:
158.37 x 2 = 316.74ft^2
total area per paint can = 20ft^2
total number of cans needed = 316.74 / 20 = 15 paint cans
Answer:
6 cans are needed to paint the dog house.
Step-by-step explanation:
WORK PROBLEMS Ted can mow the lawn in 5 minutes by using his power mower. Galen takes 15 minutes to mow the same lawn using a push-type mower. How many minutes would the job take if the two boys worked together
Ted can mow the lawn in 5 minutes by using his power mower. Galen takes 15 minutes to mow the same lawn using a push-type mower.
Let's calculate the amount of work done by Ted in 1 minute.WORK = 1/5Let's calculate the amount of work done by Galen in 1 minute.WORK = 1/15
Let's calculate the amount of work done by both of them working together in 1 minute. WORK = 1/5 + 1/15 Simplify, LCM of 5 and 15 = 15 So, 3/15 + 1/15 = 4/15Hence, working together Ted and Galen can mow the lawn in 15/4 or 3.75 minutes or 3 minutes and 45 seconds.
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A sample of a radioactive isotope had an initial mass of 690 mg in the
year 1997 and decays exponentially over time. A measurement in the
year 2001 found that the sample's mass had decayed to 390 mg. What
would be the expected mass of the sample in the year 2011, to the
nearest whole number?
Answer:
its 94 on deltamath just did it
Step-by-step explanation:
Let t=0 represent the year 1997
Starting Value: 690
Write function:
y=690(b)^t
Now find the b-value:
y=390 when t=4 (2001−1997)
390=690(b)^4
390/690=690(b)^4/690
0.56521739=b^4
(0.56521739)^1/4=(b^4)^1/4
0.86706944=b
Write Complete Function:
y=690(0.86706944)^t
Find value in 2011 (use t=14):
y=690(0.86706944)^14
y=93.67062063
y≈94
a 5 ft long ladder is leaning against a wall, and the top of the ladder is originally at 4 ft above the ground. the bottom of the ladder is being pulled away from the wall at a constant rate. how fast is the bottom of this ladder being pulled away from this wall if the top of the ladder is sliding down at a rate of 1 ft/second?
The speed at which the bottom of the ladder is being pulled away from the wall is equal to the rate at which the top is sliding down, which is 1 ft/second.
The bottom of the ladder is being pulled away from the wall at the same rate at which the top of the ladder is sliding down the wall. As the top of the ladder slides down at a rate of 1 ft/second, the bottom of the ladder is also being pulled away at a rate of 1 ft/second.
The bottom of the ladder is being pulled away from the wall at a rate of 100 ft/second if the top of the ladder is sliding down at a rate of 100 ft/second.
The speed at which the bottom of the ladder is being pulled away from the wall is equal to the rate at which the top is sliding down, which is 1 ft/second.
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22.
A map has a scale of 1 inch : 20 miles. If two
cities are 240 miles apart, how far apart are
they on the map?
NEED HELP FAST!!
Answer:
12
Step-by-step explanation:
1 inch = 20 miles
240 miles ÷ 20 miles =
12 inches
Answer:
12 inches
Step-by-step explanation:
Hey there!
Well to solve the given question we need to use fractions,
if 1 inch is 20 milles, we can set up the following.
\(\frac{1}{20} = \frac{x}{240}\)
Cross multiply
240 = 20x
Divide both sides by 20
x = 12
So it is 12 inches in the map.
Hope this helps :)
Please I need somone's help with this problem
Answer:
wich problem i see multiple ?
Maggie walked 3/5 mile in 1/2 hour. How fast did she walk, in miles per hour?
Answer:
The speed of Natalie in miles per hour is 1.2 mph.
Step by step explanation:
distance covered by Natalie, d = 3/5 mile
time of motion of Natalie, t = 1/2 hour
speed = distance/time
speed = 3×2/5 = 6/5
Thus, the speed of Natalie in miles per hour is 1.2 mph.
An artist is going to cut four similar right triangles from a rectangular piece of paper like the one shown to the right. What is BE to the nearest tenth when AC=13
The measurement of altitude BE is 4 unit.
What is an altitude?As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.
As ABCD is rectangle
AD = BC = 12
ΔABC = ΔBCD
BE = FD
5² = 3²+BE²
AE = 3
BE = √(5²-3²)
BE = 4
Thus, The measurement of altitude BE is 4 unit.
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An elementary school is offering 3 language classes one in spanish one in french, if 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
The probability that atleast one students is taking a language class is 0.7
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Let :
Spanish = S ; French = F ; German = G
SnFnG = 3
(SnF) only = 9 - 3 = 6
(SnG) only = 5 - 3 = 2
(FnG) only = 5 - 3 = 2
S only = 28 - (6+3+2) = 17
F only = 21 - (2+3+2) = 14
G only = 12 - (6+3+2) = 1
Student not taking any of the classes are;
(100 - (17+14+1+2+2+6+3))
100 - 45 = 55
Atleast 1 is taking a language class out of 2 selected
The probability that atleast one students is taking a language class :
(45/100 * 55/99) + (55/100 * 45/99) + (45/100 * 44/99)
= 0.7
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