Exponents power of power multiplication properties
(4a³b^4)³
The expression (4a³b^4)³ when evaluated is 64a^9b^12
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
(4a³b^4)³
When expanded, we have
(4a³b^4)³ = 4³ * (a³)³ * (b^4)³
Evaluate the exponents
So, we have the following representation
(4a³b^4)³ = 64a^9b^12
Hence, the solution si 64a^9b^12
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Lavaughn wraps a gift box in the shape of a right rectangular prism. The figure below shows a net for the gift box. 9 m 9 m 8 m 8 m 15 m 8 m 8 m How much wrapping paper did he use, in square meters?
The length of paper he used for wrapping paper is, 702 meters²
What is surface area ?Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.
To calculate the amount of wrapping paper needed, we need to find the total surface area of the gift box. The surface area of a right rectangular prism is given by the formula:
surface area = 2(lw + wh + lh)
where l, w, and h are the length, width, and height of the prism, respectively.
In this case, the dimensions of the gift box are 9 meters, 9 meters, and 15 meters, so:
surface area = 2(9 x 9 + 9 x 15 + 15 x 9)
= 2(81 + 135 + 135)
= 2(351)
= 702 square meters
Therefore, Lavaughn used 702 square meters of wrapping paper for the gift box.
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Write each as a percent. MAKE SURE YOU PUT THE % SIGN.
27) 1/2
28) 1/8
29) 1/100
30) 1/10
31) 3/8
32) 87/100
Answer:
50%
12.5%
1%
10%
37.5%
87%
Answer:
27)50%
28)12.5%
29)1%
30)10%
31)38.4%
32)87%
True or false a square is a parallelogram
True (but a parallelogram is not always a square). This is because a parallelogram is a quadrilateral with 2 pairs of parallel sides, and a square fits the requirements.
The student council has $100 to spend on decorations for the school dance. If streamers cost $3. 50 per roll and balloons cost $0. 75 each, write an inequality that represents the number of streamers x and balloons y the student council can buy.
The inequality that represents the number of streamers x and balloons y the student council can buy is given as follows:
3.50x + 0.75y ≤ 100.
How to model the inequality?Each streamer costs $3.50, hence the total cost of purchasing x streamers is given as follows:
3.5x.
Each balloon costs $0.75, hence the total cost of purchasing y balloons is given as follows:
0.75y.
Then the total cost of purchasing x streamers and y balloons is given as follows:
3.50x + 0.75y.
The amount spent can be of at most $100, hence the inequality is given as follows:
3.50x + 0.75y ≤ 100.
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the sum of all frequencies in a frequency distribution should sum to
The relative frequency is the proportion of the total numbers in a data set corresponds to a specific class interval and hence summing over all the relative frequencies must add up to 1, or 100%.
Frequency Distribution Table:The frequency distribution table is made by building the class intervals of the raw data set, specifically when too many values are occurring many times; we group similar values in the same category, according to a pre-determined range of values. It is a two-column table in which the first column consists of class intervals and the second consists of the frequency corresponding to each interval.
The frequency distribution is made when the raw data is large and when the same number is repeated many times, that is where the concept of frequency comes into play.
Since, the frequency is the count of specific numbers in a data set, the sum of all frequencies corresponding to every class interval has to be the total number of values in the data set.
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The given question is incomplete, complete question is:
What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?
The tax rate is
5.1%. How much is
the tax on $675?
Round to the nearest cent.
Warren earns $21.75 per hour and worked 36.5 hours last week and 32 hours the
week before. What is Warren's gross pay for the two weeks? Show your work.
Answer:
$1,489.88 (nearest cent)
Step-by-step explanation:
To calculate gross pay, multiply the number of hours worked by the pay per hour.
Warren worked 36.5 hours one week and 32 hours the week before.
Therefore, the total number of hours Warren worked was:
36.5 + 32 = 68.5 hoursMultiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:
68.5 × 21.75 = 1489.875Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).
Answer:
$1489.875
Step-by-step explanation:
Warren's gross pay for 36.5 hours last week can be calculated as follows:
Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875
Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:
Gross pay for 32 hours = $21.75/hour * 32 hours = $696
Adding the gross pay for the two weeks, we get:
Gross pay for 2 weeks = $793.875 + $696 = $1489.875
what is 65kgs in lbs ?
Since, 01 kilogram is approximately equal to 2.2046226218 lbs.
Therefore, 65 Kilogram is 143.3 lbs.
Pound:
Pound is the name of a series of units of mass ranging from 300 to 600 grams. It refers to an avoirdupois pound (454 grams), most commonly divided by 16 avoirdupois ounces.
Kilogram:
The kilogram or kilogram (symbol: kg) is the basic unit of mass in the SI system. It is defined equal to the mass of the International Prototype in kilograms. It is the only SI base unit that uses prefixes and is still defined in terms of artifacts rather than basic physical properties. A kilogram is equivalent to £2.205 in the English system used in the United States.
According to the Question:
To find how many pounds are in kilograms, you can convert kg to pounds using this formula:
X(lb) = Y(kg) / 0.45359237
Now,
Converting 65 kg to lbs:
To convert 65 kg to pounds:
⇒ X(lbs) = 65(kg) / 0.45359237
⇒ 143.3005 lbs
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What is the value of the geometric mean of the numbers 3, 4, and 18?
A. 8 1/3
C. 8 2/3
B. 8
D. 6
E. 5.5
You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect $95, selling a total of 37 jewelry items. How many of each type did you sell?
Answer: You sold 16 bracelets and 21 necklaces
Step-by-step explanation
X# Bracelets x+y=37 -2(x+y=37) -2x-2y= -74 x+21=37
Y# Necklaces 2x+3y=95 [tex]\frac{+(2x+3y=95)}{y=21}[/tex] x=16
You sold 16 bracelets and 21 Necklaces
How to find a vector equation and parametric equations for the line segment that joins p to q?
The vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.
We have P(0, -1, 1), Q(1/2, 1/3, 1/4)
We have to find a vector equation and parametric equations for the line segment that joins P to Q.
Vector equation of a line segment joining the points with position vectors r0 and r1 is given by
r =(1 - t)r0 + tr1
Where, t ∈ [0, 1]
Here, r0 = (0, -1, 1) and r1 = (1/2, 1/3, 1/4)
So, r(t) = (1 - t)(0, -1, 1) + t(1/2, 1/3, 1/4)
r(t) = [((1 - t)(0) -1(1 - t) + 1(1 - t)] + [t/2, t/3, t/4]
r(t) = [0, (t - 1), (1 - t)] + [t/2, t/3, t/4]
On simplification,
r(t) = [(t/2 + 0), (t + t/3 - 1), (1 - t + t/4)]
r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)]
Where, t ∈ [0,1]
The parametric equations for the line segment are
x = t/2, y = -1 + 4t/3, z = 1 - 3t/4
Where, t ∈ [0, 1]
Therefore, the vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.
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The given question is incomplete, complete question is:
Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, - 1, 1), Q(1/2, 1/3, 1/4).
A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on top, where the radius of the hemisphere is to be the same length as the radius of the base of the cylinder, which is 15 feet. The height of the cylinder is 30 feet.
The farmer would like to paint the outside of the silo blue when he is finished. How much area will he have to cover to paint the outside of the silo? (Use 3.14 for pi.)
Answer:
Step-by-step explanation:
To find the surface area of the silo, we need to calculate the areas of the cylinder and hemisphere separately, and then add them together.
The formula for the surface area of a cylinder is:
A_cylinder = 2πrh + 2πr^2
where r is the radius of the base of the cylinder, and h is the height of the cylinder.
In this case, r = 15 feet and h = 30 feet, so we have:
A_cylinder = 2π(15)(30) + 2π(15)^2
A_cylinder = 900π + 450π
A_cylinder = 1350π
The formula for the surface area of a hemisphere is:
A_hemisphere = 2πr^2
where r is the radius of the hemisphere.
In this case, the radius of the hemisphere is also 15 feet, so we have:
A_hemisphere = 2π(15)^2
A_hemisphere = 450π
To find the total surface area of the silo, we add the surface areas of the cylinder and hemisphere:
A_total = A_cylinder + A_hemisphere
A_total = 1350π + 450π
A_total = 1800π
Using 3.14 for π, we can approximate the total surface area as:
A_total ≈ 5652 square feet
Therefore, the farmer will need to cover approximately 5652 square feet of surface area to paint the outside of the silo.
Can somebody explain how to solve -4(2a+7)+3a+18? What type of polynomial is it?
Simplified form of the polynomial -4(2a+7)+3a+18 is -5a - 10. It is a binomial.
What is polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given expression,
-4(2a+7)+3a+18
using distributive property
-4(2a) -4(7) + 3a + 18
-8a - 28 + 3a + 18
Solving like terms
-5a - 10
The solved polynomial is a binomial, since it has two terms.
Hence, simplified form of the given polynomial is -5a - 10, it is a binomial
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A
65%
B
Reflex Angle B =
degrees.
The reflex of angle A is 295 therefore, angle B is 295°
What is a reflex angle?A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.
Given that angle B is the reflex angle of angle A, angle is measuring 65°
We need to find the measure of reflex Angle B
We know that,
To find the reflex angle of a given angle, we need to subtract the given measure from 360 degrees.
For example, the reflex angle of 110 degrees = 360 – 110 = 250.
Therefore,
Reflex Angle B = 360° - 65° = 295°
Hence, the reflex of angle A is 295 therefore, angle B is 295°
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Mrs. Chen wrote two checks and made a deposit of $1,987.09 since her october statement. The october statement shows a balance of $3,611.08, and her checkbook shows she currently has $2,778.09. What is the total amount of the checks that Mrs. Chen wrote?
A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall, then how long will the maple tree's shadow be?
The length of the shadow of the maple tree will be 15 meters.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall.
Let 'S' be the shadow of the maple tree. Then the equation is given as,
16 / 30 = 8 / S
0.533 = 8 / S
S = 8 / 0.533
S = 15 meters
The length of the shadow of the maple tree will be 15 meters.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction barts).
In the given diagram, ARST is a right triangle with MPL ST. Segment RT is divided into 5 equal parts.
R(4.3,7.4)
T(-8.5,-2.2)
M
S(4.3,-2.2)
The coordinates of point O are (
), and the coordinates of point M are (
The coordinates of P are (-0.82, 3.56).
The coordinates of M are (-2.1, -2.2).
What is a midpoint of a line segment?The midpoint of a line segment is written as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) are the coordinates of the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
R = (4.3, 7.4)
T= (-8.5, -2.2)
S = (4.3, -2.2)
Segment RT is divided into 5 equal parts.
So,
TP : PR = 3 : 2 = m : n
The coordinates of P.
T= (-8.5, -2.2) = (a, b)
R = (4.3, 7.4) = (c, d)
x = [tex]\frac{mc + na}{m + n}[/tex]
x = [tex]\frac{3\times4.3 + 2\times-8.50}{5}[/tex]
x = [tex]\frac{12.9 - 17}{5}[/tex]
x = [tex]\frac{-4.1}{5}[/tex]
x = -0.82
And,
y = [tex]\frac{md + nb}{m + n}[/tex]
y = [tex]\frac{3\times7.4 + 2\times-2.2}{5}[/tex]
y = [tex]\frac{22.2 - 4.4}{5}[/tex]
y = 3.56
The coordinates of P are (-0.82, 3.56).
Now,
T= (-8.5, -2.2)
S = (4.3, -2.2)
M is the midpoint of TS.
So,
M = (x, y)
x = [tex]\frac{(4.3 - 8.5)}{2}[/tex] = [tex]\frac{x-4.2}{2}[/tex] = -2.1
y = [tex]\frac{-2.2 - 2.2}{2}[/tex] = [tex]\frac{-4.4}{2}[/tex] = -2.2
M = (x, y) = (-2.1, -2.2)
Thus,
The coordinates of P = (-0.82, 3.56).
The coordinates of M = (-2.1, -2.2).
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Answer:
The answer is (-3.38,1.64),(-0.82,-2.2)
Step-by-step explanation:
I just got it right on the test
round the number 125.3546 to 1 decimal place
Answer: 125.4
llllljkjkjkjkkjkjkjkjkjkkjkjjkjkjkjkjkjkjjkjkjkjkjkkjkjkjjkjkjjkjkjkjkjkjkjkjkjkjkjkjkjkjjkjkjkjkjkjkjkjkjkjkkjjkkjkjkjkjkkjkjkjkjkjkjjkjkkjkjkjkjkjkjkjkjkjkjkjkkjkjkjkjkjkjkjkjkj
On a certain hot summer's day, 353 people used the public swimming pool. The daily prices are 1.50 for children and 2.50 for adults. The receipts for admission totaled 709. How many children and how many adults swam at the public pool that day?
Answer:
21
Step-by-step explanation:
21
stuart sold 8 couches and 11 armchairs at his furniture store yesterday he made a 10$ loss on each couch and a 12$ profit on each armchair what was his overall profit or loss
The overall profit of what Stuart sold is 52 dollars.
How to find loss and profit ?Stuart sold 8 couches and 11 armchairs at his furniture store yesterday and he made a 10 dollars loss on each couch and a 12 dollars profit on each armchair.
Therefore, the overall profit or loss can be calculated as follows:
Total loss on the couch = 8 × 10 = 80 dollars
Total profit on the armchairs = 11 × 12 = 132 dollars
Therefore,
Overall profits = 132 - 80
Overall profits = 52 dollars
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A swimming pool is 50 m in length, 30 m in breadth, and 2.5 m in depth. find the cost of cementing its floor and walls at the rate of rupees 27 per square metre?
Answer:
51,300 rupees
Step-by-step explanation:
Surface area of the 2 short walls = 2 x 30 x 2.5 = 150
Surface area of the 2 long walls = 2 x 50 x 2.5 = 250
Surface area of the floor = 50 x 30 = 1500
Total surface area = 150 + 250 + 1500 = 1900 m²
27 rupees/m² x 1900 m² = 51300 rupees
A nurse is preparing to administer dextrose 5% in water (D5W) 750 mL IV to infuse over 6 hr. The nurse should set the IV pump to deliver how many mL/hr? (Round the answer to the nearest whole number. Do not use a trailing zero. )
The nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.
Determine IV pump settingThe nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr. To calculate the infusion rate, you can use the formula:
Infusion rate (mL/hr) = Volume to be infused (mL) / Infusion time (hr)
In this case, the volume to be infused is 750 mL and the infusion time is 6 hr. Plugging these values into the formula, we get:
Infusion rate (mL/hr) = 750 mL / 6 hr = 125 mL/hr
Therefore, the nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.
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Determine the equation of a line in standard form which passes through the
point (2,-8) and perpendicular to the line-3x -9y-12.
Answer:
3x - y - 2 = 0
Step-by-step explanation:
The line-3x - 9y - 12 is given in the general form of the equation of a line, Ax + By + C = 0, where A = -3, B = -9, and C = -12.
To find the equation of the line that passes through the point (2, -8) and is perpendicular to the line-3x - 9y - 12, we need to find the slope of the perpendicular line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The slope of the line-3x - 9y - 12 can be found using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Rearranging the general form equation:
-3x - 9y - 12 = 0
9y = 3x + 12
y = (3/9)x + 4
The slope of the line is m = 3/9. To find the slope of the perpendicular line, we find the negative reciprocal:
m_perpendicular = -1 / (3/9) = -9 / 3
We have the slope of the perpendicular line, now we need to find its equation. To do this, we use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is the point through which the line passes and m is the slope of the line. Plugging in the values for the point (2, -8) and the slope -9/3:
y - (-8) = -9/3 (x - 2)
y + 8 = -3x + 6
3x - y - 2 = 0
Need help on this exit ticket
Using the secant-secant and tangent-secant formulas, the indicated measures are:
1. x = 1
2. y = 10.
3. SU = 30
4. x = 4
5. x = 1
6. CD = 12
How to Apply the Secant-secant and Tangent-secant Formula?The secant-secant and tangent-secant formulas relates the lengths of the segments formed when two secants or a secant and a tangent intersect outside a circle.
Using the formula, we can solve for the indicated measures as explained below.
1. To find x, apply the secant-secant formula:
(7 + 17) * 7 = (13x + 8x) * 8x
168 = 168x²
168/168 = 168x²/168
1 = x²
x = 1
2. To find y, apply the tangent-secant formula:
20² = y * (y + 30)
400 = y² + 30y
y² + 30y - 400 = 0
Factorize:
(y - 10)(y + 40) = 0
y = 10 or y = -40
y cannot be negative so, y = 10.
3. Apply the secant-secant formula to find the value of x:
(x + 10 + 9) * 9 = (x + 6 + 10) * 10
(x + 19) * 9 = (x + 16) * 10
9x + 171 = 10x + 160
9x - 10x = -171 + 160
-x = -11
x = 11
SU = x + 19 = 11 + 19
SU = 30
4. Apply the tangent-secant formula:
6² = x(x + 5)
36 = x² + 5x
x² + 5x - 36 = 0
Factorize:
(x - 4)(x + 9) = 0
x = 4 or x = -9
x must be positive, therefore, x = 4
5. Apply the secant-secant formula to find x:
18*10 = 20x * 9x
180 = 180x²
1 = x
x = 1
6. Apply the tangent-secant formula:
AB² = (CD + AC) * AC
Substitute the values:
8² = (CD + 4) * 4
64 = 4CD + 16
64 - 16 = 4CD
48 = 4CD
48/4 = CD
12 = CD
CD = 12
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1. Which expression defines the arithmetic series 10 +7+4+... for six terms?
your question is incomplete!
What is the cost of nuclear, coal, gas, wind, hydel, and sun electricity separately
Step-by-step explanation:
Nuclear: 6-20 cents per kWh
Coal: 5-17 cents per kWh
Gas: 5-15 cents per kWh
Wind: 2-9 cents per kWh
Hydro: 5-20 cents per kWh
Solar: 10-20 cents per kWh
Suppose that you would like to select a sample of 50 students at your school in order to learn something about how many hours per week, on average, students at your school spend engaged in a particular activity (such as studying, surfing the web, or watching TV)
To select a sample of 50 students at your school in order to learn something about how many hours per week, on average, students at your school spend engaged in a particular activity, you could use random sampling.
Random sampling involves selecting a sample of individuals from a larger population in a way that ensures each individual has an equal chance of being selected. This helps ensure that the sample is representative of the larger population and can provide accurate results.
Here are the steps you could follow to select a random sample of 50 students at your school:
1. Obtain a list of all the students at your school. This could be a roster or a directory.
2. Assign each student a unique number.
3. Use a random number generator to select 50 numbers from the list of student numbers.
4. Select the students whose numbers were chosen by the random number generator as your sample.
By following these steps, you can ensure that your sample is randomly selected and representative of the larger population of students at your school. This will allow you to accurately estimate how many hours per week, on average, students at your school spend engaged in a particular activity.
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How do you write 0.11111 as a fraction?
Answer:
Step-by-step explanation:1/9
A town's population of 25000 is expected to decrease at a rate of 6.5% per year. What will the population be in 10 years. Round your answer to the nearest whole number.
The population of the town after 10 years is expected to be about 12766
What will the population be in 10 years.We can use the formula for exponential decay to find the population of the town after 10 years.
The formula is:
P = P₀ * (1 - r)^t
Where P₀ is the initial population, r is the annual decay rate as a decimal (in this case, r = 0.065), t is the time in years, and P is the population after t years.Substituting the given values into the formula, we get:
P = 25000 * (1 - 0.065)^10
Simplifying and evaluating using a calculator:
P = 12766
Hence, the population is expected to be about 12766 .
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