(a). Rounded to three significant figures, the length of the side of the cube is 30.0 cm.
(b). Rounded to three significant figures, the height of the trapezoidal prism is 2.75 cm.
Let's solve this problem step by step:
First, let's calculate the volume of the fish tank when it is filled with water to two-thirds of its height.
The base dimensions of the fish tank are 72 cm by 48 cm, and the height is 52 cm.
Filling it with water to two-thirds of the height means the water level is at 2/3 × 52 = 34.67 cm.
The volume of a rectangular prism (the fish tank) is given by V = length × width × height.
Plugging in the values, we have V = 72 cm × 48 cm × 34.67 cm
≈ 112,430.08 cm³.
Now, let's calculate the volume of the cube.
The cube is placed in the fish tank the water level rises to three-quarters of the height is 3/4 × 52 = 39 cm.
The volume of the water that spilled can be calculated by subtracting the volume of the fish tank before the cube was placed from the volume of the fish tank after the cube was placed.
The volume of the cube is 112,430.08 cm³ - 39 cm × 72 cm × 48 cm = 28,861.92 cm³.
Since the volume of a cube is given by V = side³, we can solve for the length of the side of the cube.
Thus, side³ = 28,861.92 cm³ and by taking the cubic root of both sides, we find side ≈ 30.042 cm.
Now, let's calculate the height of the trapezoidal prism.
We know that the volume of water spilled when the trapezoidal prism is placed is 500 cm³.
Since the volume of a trapezoidal prism is given by V = (1/2) * (a + b) * h * base a and b are the lengths of the parallel sides of the trapezoid, h is the height of the trapezoid, and base is the distance between the parallel sides, we can rearrange the formula to solve for the height:
h = (2 × V) / ((a + b) × base).
The cross-sectional area of the trapezoidal prism is 928 cm², we can find the base.
Since the area of a trapezoid is given by A = (1/2) × (a + b) × h, we can rearrange the formula to solve for the base:
base = (2 × A) / (a + b).
Plugging in the values, we have base = (2 × 928 cm²) / (72 cm + 48 cm)
≈ 9.28 cm.
Now we can calculate the height of the trapezoidal prism:
h = (2 × 500 cm³) / ((72 cm + 48 cm) × 9.28 cm)
≈ 2.754 cm.
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The figure shows a circle with center
P
, a diameter
¯¯¯¯¯¯
B
D
, and inscribed
△
B
C
D
.
P
C
=
10
.
Let
m
∠
C
B
D
=
(
x
)
°
and
m
∠
B
C
D
=
(
x
+
54
)
°
.
From the given information, we have:
PC = 10 (length of segment PC)
∠CBD = x°
∠BCD = x + 54°
We can determine the relationship between angles ∠CBD and ∠BCD by recognizing that they are inscribed angles intercepting the same arc CD. In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we have:
∠BCD = 1/2(arc CD)
Since ∠BCD = x + 54° and arc CD is the diameter, which is 180°, we can set up the following equation:
x + 54 = 1/2(180)
Simplifying the equation:
x + 54 = 90
x = 90 - 54
x = 36
So, the measure of ∠CBD (m∠CBD) is 36°.
Plot the points A(- 1, - 1); B(9, 2) * C(2,- 6) on the coordinate axes below. State the coordinates of point D such that A, B, C, and D would form a parallelogram .
What is true about the graph below? Select SIX TRUE statements
Select ALL TRUE statements
A) There are no zeroes
B) There is one zero
C) There are two zeroes
D) The vertex is (1, 14)
E) The vertex is (14, 1)
F) The vertex is (2, 14)
G) The vertex is (14, 2)
H) The axis of symmetry is x = 1
I) The axis of symmetry is x = 2
J) The "a" of the parabola is positive
K) The "a" of the parabola is negative
M) The parabola has a minimum
N) The parabola has a maximum
O) The zeroes are -2 and 6
P) The zeroes are 1 and 6
Q) The zero is 6
R) The zero is 14
For the given parabola the zeroes are -2 and 6, the axis of symmetry is x = 2, the parabola has a maximum and the vertex is (2, 14)
The given figure is a parabola, a plane curve which is mirror-symmetrical and is approximately U-shaped is called parabola
The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis).
The zeroes are -2 and 6
The parabola has a maximum as the vertex has posititve
The axis of symmetry for a parabola is the line which will separate a parabola into two equal halves
The axis of symmetry is x = 2
The vertex of a parabola is the point of intersection of the parabola and the axis of symmetry.
The vertex is (2, 14)
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Can yall help me with this pls i really need help with it
(x + 12)° + (5x)° = 90°
m∠1 = 25° and m∠2 = 65°
Step-by-step explanation:We know that the little box represents 90 degrees. We will write an equation using this information.
(x + 12)° + (5x)° = 90°
Next, we will solve by isolating the x variable with inverse operations and combing like terms.
(x + 12)° + (5x)° = 90°
x° + 5x° = 78°
6x° = 78°
x = 13°
Lastly, we will find the value of each angle by substituting.
m∠1 = (x + 12)° = ((13) + 12)° = 25°
m∠2 = (5x)° = (5(13))° = 65°
give me the answer for the problem
Answer:
[tex]-8x^3\sqrt{7}[/tex]
Step-by-step explanation:
Step 1: Let's start by simplifying -4x^2 * (√63x^2) using the following steps:
1.1: Separate √63x^2 into two terms:
-4x^2 * (√63 * √x^2)
1.2: Find the largest perfect square that we can factor out of 63. It's 9 as 3^2 = 9 and 9 * 7 = 63. Furthermore, √x^2 simplifies to x:
-4x^2 * (√9 * 7 * (x))
-4x^2 * (3√7 * x)
1.3: We can multiply x and 3:
-4x^2 * (3x√7)
1.4: We can distribute -4x^2 to 3x√7.
Multiplying the coefficients will give us -12 as -4 * 3 = 12.x^2 * x = x^3-12x^3 * √7
Step 2: Now we can work on simplifying x^3√112 using the following steps:
2.1: Find the largest perfect square you can factor out of 112. It's 16 since 4^2 = 16 and 16 * 7 = 112:
x^3 * √16 * 7
x^3 * 4√7
2.2: Multiply x^3 and 4√7:
4x^3 * √7
Step 3: Thus, -4x^2 * √63x^2 simplified individually is -12x^3 * √7 and x^3 * √112 simplified individually is 4x^3 * √7
3.1: Add -12x^3 * √7 + 4x^3 * √7:
-8x^3√7
Optional Step 4: We can check that we've correctly simplifed the equation by plugging in a number for x in both the radical expression not yet simplified and the simplified radical expression. If we get the same answer, then we've simplified the expression correctly. We can plug in 2 for x.
Plugging in 2 for x in -4x^2 * (√63x^2) + x^3 * (√112):
(1.) -4(2)^2 * √63(2)^2 + 2^3 * √112:
(2.) -4(4) * √63(4) + 8 * √112
(3.) -16 * √252 + 8 * √112
(4.) -16 * √36 * 7 + 8 *√16 * 7
(5.) -16 (6 * √7) + 8(4 *√7)
(6.) -96 * √7 + 32 * √7
(7.) -64√7
(8.) -169.3280839
Plugging in 2 for x in -8x^3√7:
(1.) -8(2)^3 * √7
(2.) -8(8) * √7
(3.) -64 * √7
(4.) -169.3280839
Therefore, we've correctly expressed the expression in simplest radical form
1. The population of a town was 112 in 2014. The population doubles every year.
(a) Use the exponential growth model to write an equation that estimates the population t years after 2014.
(b) Estimate the population of the town in 2023.
Show your work.
Answer:
Answer: 2048
Step-by-step explanation: 1. Write the exponential growth model.
The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.
2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048
Therefore, the estimated population of the town in 2023 is 2048.
What is the simplest
Answer:
(c) x³·∛x
Step-by-step explanation:
You want the simplified form of ∛(x¹⁰).
Cube rootsThe first part of the problem tells you how to get there. After you have that expression, you need to bring the x⁹ term from under the radical.
[tex]\sqrt[3]{x^{10}}=\sqrt[3]{x^9\cdot x}=\sqrt[3]{x^9}\cdot\sqrt[3]{x}=\boxed{x^3\cdot\sqrt[3]{x}}\qquad\text{matches choice C}[/tex]
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If tan (theta)=-2.1, what is the value of theta to the nearest whole degree?
Answer:
-65°
Step-by-step explanation:
You want the angle whose tangent is -2.1.
ArctangentThe inverse tangent function is used to find the angle when the tangent is known. On your calculator, the key for this will likely be labeled tan⁻¹. You need to make sure the calculator mode is set to degrees.
The value of θ is about -65°.
__
Additional comment
The principal branch of the arctangent function extends from -90° to +90°. The tangent function is periodic with period 180°, so adding any integer multiple of 180° to -65° will give you another angle whose tangent is -2.1. One such angle is 115°.
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What is the value of r
Step-by-step explanation:
Vertical angles are equal r = 70 degrees
help me..... its due today
Answer:
a. q^2 = sqr(225) can be solved.
q^2 = sqr(225) means q^2 = 15^2. So, q can be found by taking the square root of both sides:
q = ±15
Step-by-step explanation:
Explain the meaning of the scale 1:1000 in words
15 pies a m regla de 3
Answer:
5m
Step-by-step explanation:
regla de 3:
1m = 3ft
15 pies ÷ 3 = 5m
Given sin a = 8/17
Calculate tan a
Answer:
8/15
Step-by-step explanation:
Assuming that a is in the 1st quadrant, based on sin a = 8/17 you can build a right triangle as in the picture. Third side you compute with Pythagoras [tex]x^2 + 8^2 = 17^2 \implies x = 15[/tex].
At this point the tangent is the ratio of the two segments, or 8/15.
Else, you can calculate cos a based on the fact that [tex]cos\ a = \sqrt{1-sin^2\ a}[/tex] (under the same assumption as the beginning. Then it's just a matter of plugging numbers.
Write the expression for the following statement without
any spaces: There are z fish in the aquarium. one-fourth
of the fish are angelfish: how many are not angelfish can
be expressed as
The expression implies that the number of fish that are not angelfish can be represented as 3/4
In this expression, "z" represents the total number of fish in the aquarium. The statement mentions that one-fourth of the fish are angelfish, which means that 1/4 of "z" fish are angelfish.
To determine how many fish are not angelfish, we need to subtract the number of angelfish from the total number of fish. Since 1/4 of the fish are angelfish, 3/4 of the fish must be non-angelfish.
Therefore, the expression implies that the number of fish that are not angelfish can be represented as 3/4 of "z," which can be mathematically written as (3/4)z.
In summary, the expression represents the number of fish that are not angelfish based on the total number of fish "z" in the aquarium.
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30 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1 MANGO FRUIT IS EQUIVLENT TO HOW MANY CUBES OF SUGAR, KNOWING THAT EACH CUBE WEIGHTS 5 GRAMS?
Answer:
Step-by-step explanation: To determine the number of cubes of sugar equivalent to one mango fruit, we need to know the weight of a mango. Since you haven't provided that information, I cannot give you an accurate answer. However, on average, a medium-sized mango weighs around 150-200 grams. If we assume the weight of the mango is 150 grams, we can calculate the number of sugar cubes:
150 grams ÷ 5 grams/cube = 30 cubes
Therefore, if a mango weighs around 150 grams, it would be roughly equivalent to 30 cubes of sugar, assuming each cube weighs 5 grams.
if x= -4 calculate the value of: 2x squared -5
Answer:
2x squared - 5
= 2(x)^2 - 5
= 2(4)^2 - 5
= 2(16) - 5
= 32 - 5
= 27
Wooden poles produced for electricity networks in rural areas have lengths that are normally distributed. 2% of the poles are rejected because they are considered too short, and 5% are rejected because they are too long.a. Find the mean and standard deviation of these poles if the acceptable range is between
6.3 m and 7.5 m.b. In a randomly selected sample of 20 poles, find the probability of finding 2 rejected poles.
Answer:
a. Let X be the length of a wooden pole produced for electricity networks in rural areas. The probability of a pole being rejected because it is too short is 0.02, and the probability of a pole being rejected because it is too long is 0.05. The acceptable range is between 6.3 m and 7.5 m. We can find the mean and standard deviation of X as follows:
First, we need to find the z-score corresponding to the lower bound of the acceptable range:
z1 = (6.3 - μ) / σ
Similarly, we need to find the z-score corresponding to the upper bound of the acceptable range:
z2 = (7.5 - μ) / σ
Using a standard normal table, we can find the values of z1 and z2 that correspond to the probabilities of 0.02 and 0.95, respectively:
z1 = -2.05
z2 = 1.64
Solving for μ and σ, we get:
z1 = (6.3 - μ) / σ => μ = 6.3 + 2.05σ
z2 = (7.5 - μ) / σ => σ = (7.5 - 6.3) / 1.64 = 0.74
Therefore, the mean and standard deviation of X are:
μ = 6.3 + 2.05(0.74) = 7.6 m
σ = 0.74 m
b. Let Y be the number of rejected poles in a sample of 20 poles. Y follows a binomial distribution with parameters n = 20 and p = 0.02 + 0.05 = 0.07. The probability of finding 2 rejected poles in a sample of 20 poles is:
P(Y = 2) = (20 choose 2) * 0.07^2 * 0.93^18 = 0.242
The probability of finding 2 rejected poles in a sample of 20 poles is 0.242.
PLEASE HELP ASAP WILL GIVE 50 PTS AND BRAINLIEST :) thank u !!
Answer:
a is g(x) b is f(x)
Step-by-step explanation:
because a increases faster
A Car moves 45km in 45 min.What
is it speed in kilometres per hour
Hello !
45min = 3/4h = 0,75h
[tex]\frac{45km}{0,75h} \\\\= \frac{45km*\frac{1}{0,75} }{0,75h*\frac{1}{0,75} } \\\\= \frac{60km}{1h}[/tex]
s = 60km/h
[tex]s=\dfrac{d}{t}\\\\d=45\text{ km}\\t=45\text{ min}=0.75\text{ h}\\\\s=\dfrac{45\text{ km}}{0.75\text{ h}}=60\dfrac{\text{km}}{\text{h}}[/tex]
Rectangles QRSP and UVST are congruent. Rectangle QRSP can be rotated 90 degrees clockwise onto rectangle UVST. what point is the center of rotation? explain why. Please help I will mark you brainliest!
Answer:
C. S
Step-by-step explanation:
You want the center of rotation when figure QRSP is rotated 90° CW to become UVST.
Center of rotationThe center of rotation is the point of coincidence of the perpendicular bisectors of the segments between a preimage point and the corresponding image point. It is also the only point on the plane that is invariant with the rotation.
The rectangle names tell us the rotation maps the points as follows:
Q ⇒ UR ⇒ VS ⇒ S . . . . . . an invariant pointP ⇒ TThe fact that point S does not move tells us that it is the center of rotation. As a check, we can see if the perpendicular bisectors of QU, RV and PT intersect at point S. (They do.)
Point S is the center of rotation.
__
Additional comment
Unfortunately, the image attached to the problem statement distorts the lines and angles. Hence, it cannot be used to find the precise location of the center of rotation. (In fact, the "rectangles" shown are only conceptual rectangles, not actual congruent rectangles.)
The perpendicular bisector of QU seems to pass through S, as it must if S is the center of rotation.
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Find angles A, B, C and D
Answer: a=101 b=79 c=83 d=97
The diagram shows a scale drawing of the
side elevation of a building.
3 cm represents 1 m.
What is the width of the building in metres?
(Give your answer in meters).
Please answer, and no spam.
Answer:
The answer for the width of the building 5m
Step-by-step Explanation:
3cm=1m
15cm=x
cross multiply
x×3=15×1
3x=15
divide both sides by 3
3x/3=15/3x=5m
pls help will mark brainleist
Answer:
x = 48°
Step-by-step explanation:
[tex]x=(90-42)^{0} =48^{0}[/tex]
Hope this helps
★ The sum of the angles in a triangle is always 180° ...
➺ 42° + x + 90° = 180°➺ 42° + 90° + x = 180°➺ 132° + x = 180°➺ x = 180° - 132° ➺ x = 48°________________________________
What the meaning of statement this?
If p(x) ⊆ p(y), then it means that every element of the power set of x is also an element of the power set of y. This implies that set x is a subset of set y, written as x ⊆ y.
Here,
Let A be the set x and B be the set y. Then the power sets of A and B are p(A) and p(B) respectively.
Suppose p(A) ⊆ p(B). This means that for every element a in p(A), a is also an element of p(B).
Now consider any element a in A. Since a is an element of A, it is also an element of its power set p(A). Thus, if p(A) ⊆ p(B), a must also be an element of p(B). This means that a is an element of B.
Therefore, we have established that every element of A is an element of B. That is, A ⊆ B.
Thus, if p(x) ⊆ p(y), then x ⊆ y.
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Help plssssssss 3+4x2
Answer:
The expression 3+4x2 can be simplified using the order of operations, which is a set of rules used to determine the sequence in which operations are performed in an expression. According to the order of operations, we first perform any calculations inside parentheses, then we perform any multiplications or divisions (from left to right), and finally we perform any additions or subtractions (from left to right).
There are no parentheses in this expression, so we move on to the next step, which is to perform any multiplications or divisions. In this case, we have 4x2, which equals 8. So, we can replace 4x2 with 8, and the expression becomes:
3+8
Finally, we perform the addition, and get the final result:
11
Therefore, 3+4x2 is equal to 11.
Step-by-step explanation:
Can yall hel me with this pls
Answer:
X = 10
Z = 67
Step-by-step explanation:
We see that the angles are formed by the intersection of two lines.
Angles z and 67° are vertically opposite angles and therefore they are equal to each other
z°= 67°
Angles z and (7x + 43) are supplementary angles. The sum of these angles add up to 180°
z + 7x + 43 = 180
67 + 7x + 43 = 180
7x + 110 = 180
7x = 180 -110 = 70
x = 70/7 = 10
6x^7+3x^4-9x^3 factor
Answer:
[tex]3x^3(x-1)(2x^3+2x^2+2x+3)[/tex]
Step-by-step explanation:
We can start by factoring out x³ because it's the greatest factor of every term:
[tex]6x^7+3x^4-9x^3=x^3(6x^4+3x-9)[/tex]
Next, notice that each coefficient is divisible by 3, so this can be factored out as well:
[tex]x^3(6x^4+3x-9)=3x^3(2x^4+x-3)[/tex]
While it may not look like we can factor out 2x⁴+x-3, we actually can! Notice the following:
[tex]2x^4+x-3=(2x^4+2x^3+2x^2+3x)+(-2x^3-2x^2-2x-3)=x(2x^3+2x^2+2x+3)-1(2x^3-2x^2+2x+3)=(x-1)(2x^3+2x^2+2x+3)[/tex]
By grouping, we were able to condense this factor. Thus:
[tex]6x^7+3x^4-9x^3=\bf{3x^3(x-1)(2x^3+2x^2+2x+3)}[/tex]
Find the total in the retirement account given the following conditions:
Monthly contributions = $225
Interest rate = 4.99%
Years invested = 38
To find the total in the retirement account after 38 years of investing with monthly contributions and an interest rate of 4.99%, we can use the compound interest formula.
The formula for the future value of an investment with regular monthly contributions is given by:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value or the total in the retirement account.
P is the monthly contribution amount.
r is the monthly interest rate (annual interest rate divided by 12).
n is the number of monthly contributions (years invested multiplied by 12).
Let's calculate the total:
P = $225
r = 4.99% / 100 / 12 = 0.0041583 (monthly interest rate)
n = 38 * 12 = 456 (number of monthly contributions)
FV = $225 * [(1 + 0.0041583)^456 - 1] / 0.0041583
Using a financial calculator or spreadsheet, we can evaluate this expression to find the future value or total in the retirement account.
The calculated total may vary depending on the compounding frequency and rounding used.
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite
direction. The number b varies directly with the number a. For example b = 2 when a = -2
-22. Which equation
represents this direct variation between a and b?
b=-a
-b=-a
b-a=0
b(-a) = 0
Mark this and return
Next
Submit
The equation that represents the direct variation between a and b in this scenario is: b = -a.
The correct option is (A).
We have,
The number b varies directly with the number a.
This equation states that b is equal to the negative value of a, which reflects the condition that b is located in the opposite direction from 0 compared to a and varies directly with a.
So, the equation cab be stated as b = -a.
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If firefighters response time to an emergency call is normally distributed with a mean of 9 minutes and a standard deviation of 2 minutes. Determine the percent of emergency calls with a firefighter response time between 7 and 11 minutes.
They are 68.27% of emergency calls have a firefighter response time between 7 and 11 minutes.
To determine the percentage of emergency calls with a firefighter response time between 7 and 11 minutes, we need to calculate the area under the normal distribution curve between these two values.
First, let's standardize the values of 7 and 11 using the z-score formula:
z1 = (7 - mean) / standard deviation
= (7 - 9) / 2
= -2 / 2
= -1
z2 = (11 - mean) / standard deviation
= (11 - 9) / 2
= 2 / 2
= 1
Next, we can use a standard normal distribution table or a statistical calculator to find the area under the curve between these z-scores.
The area between z = -1 and z = 1 represents the percentage of emergency calls with a firefighter response time between 7 and 11 minutes.
Using a standard normal distribution table, we get between z = -1 and z = 1 is approximately 0.6827.
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