Answer:
7.1ft
Step-by-step explanation:
The formula for calculating the total surface area of a cube is 2(L²+L²+L²)
=2(3L²)
= 6L²
Where L is the length of the cube
If the total surface area of a cube is 302.46ft², then
302.46 = 6L²
L² = 302.46/6
L² = 50.41
L =√50.41
L = 7.1ft
The length of the side of the cube is 7.1ft
The length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]
To find the length of the side of a cube given its total surface area, we need to use the formula for the surface area of a cube.
The formula for the surface area of a cube is:
[tex]\[ \text{Surface Area} = 6s^2 \][/tex]
where s is the length of a side of the cube.
Given the total surface area is [tex]\( 302.46 \, \text{ft}^2 \)[/tex], we can set up the equation:
[tex]\[ 6s^2 = 302.46 \][/tex]
To solve for s we first divide both sides by 6:
[tex]\[ s^2 = \frac{302.46}{6} \][/tex]
[tex]\[ s^2 = 50.41 \][/tex]
Next, we take the square root of both sides to find s
[tex]\[ s = \sqrt{50.41} \][/tex]
[tex]\[ s \approx 7.1 \, \text{ft} \][/tex]
Thus, the length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]
A garden supply store sells two types of lawn mowers. The smaller mower costs $249.99 and the larger mower costs $329.99. If 30 total mowers were sold and the total sales for a given year was $8379.70, find how many of each type were sold.
19 small mowers and 11 large mowers are sold
Solution:
Let "a" be the number of small mowers sold
Let "b" be the number of large mowers sold
Cost of each small mower = $ 249.99
Cost of each large mower = $ 329.99
30 total mowers were sold
Therefore,
a + b = 30
a = 30 - b ------------- eqn 1
The total sales for a given year was $8379.70
Thus we frame a equation as:
number of small mowers sold x Cost of each small mower + number of large mowers sold x Cost of each large mower = 8379.70
[tex]a \times 249.99 + b \times 329.99 = 8379.70[/tex]
249.99a + 329.99b = 8379.70 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
249.99(30 - b) + 329.99b = 8379.70
7499.7 - 249.99b + 329.99b = 8379.70
80b = 8379.70 - 7499.7
80b = 880
Divide both sides by 80
b = 11
Substitute b = 11 in eqn 1
a = 30 - 11
a = 19
Thus 19 small mowers and 11 large mowers are sold
The tree diagram represents an experiment consisting of two trials.
P(A and C) = [?]
Yo sup??
P(A)=0.5
P(C|A)=0.4
Therefore
P(A and C)=0.5*0.4
=0.2
Hope this helps.
The required probability is P(A and C) is 0.2 which is represented in the tree diagram.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The given tree diagram represents an experiment consisting of two trials.
The tree diagram represents an experiment consisting of two trials. In this case, the probability of event A and event C occurring is represented by the intersection of branches A and C in the tree diagram.
This probability can be calculated by multiplying the probability of each individual event together.
As per the given question, we have
P(A) = 0.5
P(C|A) = 0.4
So, P(A and C) = 0.5 × 0.4 = 0.2
Thus, the required probability is P(A and C) is 0.2
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Use the distributive property to clear parentheses.
-6(3x+4)
Answer:-18x-24
Step-by-step explanation:Use the PEMDAS method
explanation:-18x-24
The rations that are equivalent to 16:12
Answer:
4:3, 32:24, 8:6
Step-by-step explanation:
for 4:3, you divide both sides of 16:12 by 4
for 32:24 you mutiple both sides by 2
for 8:6 you multiply both sides by 2
Hope this helps :)
Paul's family drove 377 mi to the beach averaging 58 mi/h on the way there. On the return trip home, they averaged 65 mi/h.
What was the total time Paul's family spent driving to and from the beach?
11.3 h
11.6 h
12.3 h
13 h
Answer:
12.3 hours
Step-by-step explanation:
So other person can get brainliest
solve for x: 3(9-8x-4x)+8(3x+4)=11
Answer:
x=4
Step-by-step explanation:
3(9-8x-4x)+8(3x+4)=11
Subtract 4 x from − 8 x
3 ( 9 − 12 x ) + 8 ( 3 x + 4 ) = 11
Distribute
27 − 36 x + 24 x + 32 = 11
Simplify
− 12 x + 59 = 11
Subtract 59 to both sides
− 12 x = − 48
Divide by -12
x=4
Pirate Jack has an equal number of gold and silver coins. If Pirate Jack splits all of his coins into 7 equal piles for his parrots, he has 4 coins left. Or, if he splits all of his coins into 11 equal piles for his shipmates, he has 4 coins left. Assuming every pile has at least 1 coin, what is the least possible number of coins Pirate Jack has?
Answer:
The least possible number of coins that Pirate Jack has is 77.
Step-by-step explanation:
i) let the number of coins in the piles for the parrots be x.
ii) therefore we can say that the total number of coins be 7x + 4
iii) let the number of coins in the piles for for the pirates be y.
iv) therefore we can say that the total number of coins be 11y + 4
v) therefore we can say that 7x + 4 = 11y + 4
vi) therefore 7x = 11y
vii) therefore the least possible number of coins that Pirate Jack has is equal to the LCM of 11 and 7 which is 77.
viii) x = 11 and y = 7
Answer:
158 coins
Step-by-step explanation:
Jack's number has to be an even number, because he can split his gold and silver coins evenly.
77 is the LCM of 11 and 7 and add 4 (the remainder) to get 81.
But it has to be an even number since he can split his coins evenly.
You can then do 77 times 2, and add 4 to get 158, which is the answer.
How many solutions y=x^2-10x+25
Step-by-step explanation:
Given,
y = [tex]x^2[/tex] - 10x + 25
To find, the total number of solutions = ?
∴ y = [tex]x^2[/tex] - 10x + 25
⇒ y = [tex]x^2[/tex] - 2(x)(5) + [tex]5^2[/tex]
⇒ y = [tex](x-5)^{2}[/tex]
There are infinite solution of y.
Thus, there are infinite solution of y.
Can anyone help me please
Angle A and Angle B are identical, so AC and BC are also identical.
ABC = AC
3x -7 =20
Add 7 to both sides:
3x = 27
Divide both sides by 3:
x = 9
Tina is fixing a rectangular sign. She plans to place a metal trim around the sign edges. The rectangle measures 32 inches by 9 inches. How much trim will Tina need?
Answer:288
Step-by-step explanation:32 x 9 = 288
Suppose the two line segments in a coordinate plane one with a length of 120 units and other with a length of 240 units were both rotated 90 degrees about the origin and then translated 50 units up one of the resulting segments could have a length of...units.
In the image, the length of the segment will be 120 units.
Step-by-step explanation:
Whatever may be transformation, either rotation, reflection or translation, the length the line segment will not change.
Here one segment with 120 units and other segment with 240 units is rotated 90 degrees about the origin and then it is translated 50 units up, we will get the image of the segment with the same size.
In the image, the length of the segment will be 120 units.
A circle has a circumference of 56π centimeters (cm). What is the radius of the circle?
Answer:
if C = 56pi, you do plug in the given by using the formula C = 2pi(r)
56pi = 2pi(r)
56/2 = r
r= 28
the radius is 28
Make Q the subject of formula.
[tex]T=\sqrt{\frac{PQ}{R} }-R^{2}Q[/tex]
Answer:
Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))
Step-by-step explanation:
Solve for Q:
T = sqrt((P Q)/R) - Q R^2
T = sqrt((P Q)/R) - Q R^2 is equivalent to sqrt((P Q)/R) - Q R^2 = T:
sqrt((P Q)/R) - Q R^2 = T
Add Q R^2 to both sides:
sqrt((P Q)/R) = Q R^2 + T
Raise both sides to the power of two:
(P Q)/R = (Q R^2 + T)^2
Expand out terms of the right hand side:
(P Q)/R = Q^2 R^4 + 2 Q R^2 T + T^2
Subtract Q^2 R^4 + 2 Q R^2 T + T^2 from both sides:
(P Q)/R - Q^2 R^4 - 2 Q R^2 T - T^2 = 0
Collect in terms of Q:
-Q^2 R^4 - T^2 + Q (P/R - 2 R^2 T) = 0
Divide both sides by -R^4:
Q^2 + T^2/R^4 - (Q (P/R - 2 R^2 T))/R^4 = 0
Subtract T^2/R^4 from both sides:
Q^2 - (Q (P/R - 2 R^2 T))/R^4 = -T^2/R^4
Add (P/R - 2 R^2 T)^2/(4 R^8) to both sides:
Q^2 - (Q (P/R - 2 R^2 T))/R^4 + (P/R - 2 R^2 T)^2/(4 R^8) = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4
Write the left hand side as a square:
(Q - (P/R - 2 R^2 T)/(2 R^4))^2 = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4
Take the square root of both sides:
Q - (P/R - 2 R^2 T)/(2 R^4) = sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
Add (P/R - 2 R^2 T)/(2 R^4) to both sides:
Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:
Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt((P^2)/(4 R^10) - (P T)/(R^7)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)
Add (P/R - 2 R^2 T)/(2 R^4) to both sides:
Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4))
(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:
Answer: Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))
The time a projectile spends in the air can be modeled by the equation t² -t - 8 = 0, in which t represents the amount of time traveled, in seconds. Which of the following is equivalent to the equation t² - 2t - 8 = 0?
(t + 4)(t - 2) = 0
t -4)(t - 2) = 0
(t + 4)(t + 2) = 0
(t - 4) (t + 2) = 0
Answer:
(t - 4)(t + 2) = 0
Step-by-step explanation:
The general formula for a quadratic expression is
y = ax² + bx + c
Your expression is
y = t² - 2t - 8 = 0
By comparison, we see that
a = 1; b = -2; c = -8
1. Find two numbers that multiply to give ac and add to give b.
In this case, find two numbers that multiply to give -8 and add to give -2.
It helps to list the factors of -8.
They are ±1, ±2, ±4, and ±8
After a little trial and error, you should find the numbers -4 and +2.
-4 × 2 = -8, and -4 + 2 = -2)
2. Rewrite the middle term with those numbers
t² -4t + 2t - 8 = 0
3. Factor the first and last pairs of terms separately
t(t - 4) +2(t - 4) = 0
4. Separate the common factor
The common factor is t - 4.
(t - 4)(t + 2) = 0
What is 12 percent of 29
Answer:
3.48
Step-by-step explanation:
12%=0.12
0.12*29=3.48
Urgent!
Write a polynomial, P(x), in factored form given the following requirements.
Degree: 3
Zeros (roots) at (−2,0) with multiplicity 2 and (3,0) with multiplicity 1
P(x) passes through the point (2,80)
Answer:
The polynomial will be P(x) = - 5 (x + 2)²(x - 3)
Step-by-step explanation:
The degree of the polynomial P(x) is 3 and it has zeros at x = - 2 with multiplicity 2 and at x = 3 with multiplicity 1.
Therefore, (x + 2)² and (x - 3) are the factors of the equation.
Let the polynomial is
P(x) = a(x + 2)²(x - 3) ........... (1)
Now, the polynomial passes through the point (2,80).
So, from equation (1) we gat,
80 = a(4)²(-1)
⇒ a = - 5
Therefore, the polynomial will be P(x) = - 5 (x + 2)²(x - 3) (Answer)
The required polynomial is [tex]P(x) = - 5 (x + 2)^{2} (x - 3)[/tex]
Any polynomial have number of roots equal to its degree of polynomial.
Since, the degree of the polynomial P(x) is 3. it means that it has 3 roots.
it has zeros at x = - 2 with multiplicity 2, it means that factor (x - 2) have power 2 and at x = 3 with multiplicity 1 means that factor (x - 3) have power of 1 .
Thus, [tex](x + 2)^{2}[/tex] and (x - 3) are the factors of the equation.
Let us consider the polynomial is [tex]P(x) = k(x + 2)^{2} (x - 3) .[/tex]
Since, the polynomial passes through the point (2,80).
So, substituting point (2, 80) in above polynomial equation.
We get, [tex]80 = a(4)^{2} (-1)[/tex]
a = - 5
Therefore, the polynomial is [tex]P(x) = -5(x + 2)^{2} (x - 3) .[/tex]
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You have 3 quarters, 7 dimes, and 5 nickles in your pocket. A coin is chosen at random. What is the BEST answer for the probability of drawing a quarter?
A) impossible
B) unlikely
C) very likely
D) certain
Answer:
B) Unlikely
Step-by-step explanation:
Your chance drawing a quarter is a low 20%
Answer:
B:Unlikely
Step-by-step explanation:
Because you have 7 dimes and 5 nickels so those ones would be more likely to be picked than the quarter but it is still possible.
Black bears lose 1/5 of the body weight during hibernation. A black bear weighs 265 poundBlack bears lose 1/5 of their body weight during hibernation. A blackK Bear weighs 260 pounds. How much weight did it lose while hibernating
Answer:
52lbs
Step-by-step explanation:
To find out how much weight the black bear lost during hibernation, subtract the weight after hibernation from the weight before hibernation: 265 - 260 = 5 pounds.
Explanation:To find out how much weight the black bear lost during hibernation, we can use the information that black bears lose 1/5 of their body weight during hibernation. We know that the black bear weighed 265 pounds before hibernation and weighs 260 pounds after hibernation. To calculate the weight loss, we subtract the weight after hibernation from the weight before hibernation: 265 - 260 = 5 pounds. Therefore, the black bear lost 5 pounds while hibernating.
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need helpppppppppppppppppppppppppppp
Answer:
lower case p
Step-by-step explanation:
The law of sines: [tex]\frac{sinA}{a} = \frac{sinB}{b}[/tex]
Therefor look for which sides and angles are accounted for. If we are given angle P, Angle R, and Side r, then Side p is the last term that fits into the law of sines equation.
A rectangle is eight inches and diagonal is ten
inches. What's the width of the rectangle?
Answer: Its width is 6inches.
Step-by-step explanation:
The given information can be used to construct a right angled triangle. Now applying the Pythagoras theorem,
10^2 = W^2 + 8^2
where w represents the width.
100 = w^2 + 64
100 - 64 = w^2
36 = w^2
find the square root of both sides,
6 = w
Therefore, w = 6 inches
Thus the width of the rectangle is 6 inches.
What is 38.96 × 15.7 with work
If y = -x² + 14x + 7 , then x = 10 is a counterexample for which conjecture?
A.
y is always positive.
B.
y is always negative.
C.
y is a function of x.
D.
The graph of y is a parabola.
Answer:
The correct answer is B
Step-by-step explanation:
If we plug in x=10 to the equation, we get y=47
Since y is positive, A is not an counterexample
Since y is a function of x, C is not an counterexample
Since the graph of y is a parabola, D is not an counterexample
Hope this helped and mark as brainliest!
Identify all the sets to which the number belongs. Choose from Rational Number, Irrational number, whole number, and integer. 1.256...
A. Rational number
B. Irrational number
C.Integer, and rational number
D. Whole number, Integer, and rational number
Answer:
The number 1.256 is A)rational number.
Step-by-step explanation:
A whole number is a non-negative number without any digits behind the decimal. An integer is a set of negative and non negative numbers that don't have any digits behind the decimal.A number that can be shown as a fraction of two whole numbers is a rational number.And the numbers that are not rational are irrational numbers.Here, 1.256 is a fraction of whole numbers 1256 and 1000 , so it is a rational no.[tex]\frac{1256}{1000} =1.256[/tex]
But since it has digits behind the decimal it is neither a whole number, or an integer.The number 1.256... is a rational number because it can be expressed as a ratio of two integers. It is not an integer, whole number, or irrational number.
Explanation:The number 1.256 repeated is a rational number because it can be expressed as the ratio of two integers, which fits the definition of a rational number as ratios of integers such as 2/1, 3/4, and so on.
Even though the decimal representation may appear to continue forever, if the pattern of digits repeats indefinitely, it is still rational.
This number is not an integer, whole number, or irrational number, so it does not belong to those sets. An integer is a whole number without any fractional or decimal part, positive or negative, including zero.
Therefore, the correct option that defines the sets to which the number 1.256... belongs is Option A: Rational number.
By definition,
|a + bi| =
Answer:
|z| = |a + ib| = [tex]\sqrt{a^{2} + b^{2}}[/tex].
Step-by-step explanation:
By the definition of complex numbers the modulus of any complex number z = x + iy is given by |z| = |x + iy| = [tex]\sqrt{x^{2} + y^{2}}[/tex].
Say for example, z = 3 + 4i is a complex number then
|z| = |3 - 4i| = [tex]\sqrt{3^{2} + 4^{2}} = 5[/tex]
In a complex plane modulus of a complex number z = x + iy means the distance of the point (x, iy) from the origin. (Answer)
The slide at the playground has a height of 6 feet.The base of the slide measured on the ground is 8 feet.what is the length of the slide
Answer: 10ft
Step-by-step explanation:
Using the Pythagorean theorem (a² + b² = c²) you would end up with an equation like this: 36 + 64 = 100. You would then square root 100 and the answer would be 10 ft
What is the probability of getting a number less than 7 on a standard six-sided die
Answer:
100%
Step-by-step explanation:
You cant get a number on a 6 sided die higher than 7.
in the equation 3/4(x+8)=9 ,what does x equal
Answer:
x=4
Step-by-step explanation:
The given equation, the value of x is :
Solving the equation
[tex]3/4(x+8)=9\\0.75(x+8)=9\\0.75x+6.00=9\\0.75x=3\\x=3/0.75\\x=4[/tex]
The value of x is 4 .
Let n represent the position of a term in the sequence below.
8, 11, 14, 17, 20, 23,
Which algebraic expression can be used to find the nth term of the sequence
The algebraic expression can be used to find the nth term of the sequence is:
[tex]a_n = 5+3n[/tex]
Where, [tex]n\geq 1[/tex] and n is a positive whole number
Solution:
Given sequence is:
8, 11, 14, 17, 20, 23
Let us find the common difference between terms
11 - 8 = 3
14 - 11 = 3
17 - 14 = 3
20 - 17 = 3
23 - 20 = 3
Thus the common difference between successive term and previous term is constant
Thus this is a arithmetic sequence
The formula for nth term term of arithmetic sequence is given as:
[tex]a_n = a_1+(n-1)d[/tex]
Where,
[tex]a_n[/tex] is the nth term of sequence
[tex]a_1[/tex] is the first term of sequence
d is the common difference between terms
Here in this sequence, 8, 11, 14, 17, 20, 23
[tex]a_1 = 8\\\\d = 3[/tex]
Therefore,
[tex]a_n = 8+(n-1)3\\\\a_n = 8+3n -3\\\\a_n = 5+3n[/tex]
Where, [tex]n\geq 1[/tex] and n is a positive whole number
Thus algebraic expression can be used to find the nth term of the sequence is found
Use the following paycheck to answer the question.
What percent of Zachary's pay do his deductions comprise?
To calculate the percentage of Zachary's pay that his deductions comprise, divide the total amount of deductions by the total pay, then multiply by 100.
Explanation:To find out what percent of Zachary's pay his deductions compromise, you need to divide the total amount of deductions by the total amount of his pay, and then multiply by 100 to get the percentage.
Let's use an example. If Zachary's total deductions are $300 and his total pay is $1000, you would do the following calculation:
Divide 300 by 1000. This will give you 0.3. Multiply 0.3 by 100. This will give you 30.
In this example, Zachary's deductions comprise 30% of his total pay.
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Y=|3x-3|-9 use x-values to find solution -1,0,4
Answer:
Step-by-step explanation: