Answer:
x^25
Step-by-step explanation:
The simplified expression is x²⁵.
Given is an expression (x⁵)⁵, we need to simplify the expression.
To simplify the expression (x⁵)⁵, we need to apply the exponentiation rules.
The exponent outside the parentheses should be distributed to each term inside the parentheses.
In this case, the exponent outside is 5, and the term inside the parentheses is x⁵.
To distribute the exponent, we multiply the exponents together.
Applying the rule, we get:
(x⁵)⁵ = x⁵⁽⁵⁾ = x²⁵
Therefore, the simplified expression is x²⁵.
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Benito earns an annual salary of $36,000. He is paid twice a month with paychecks being of equal amounts. What is the gross income that Benito will earn on his paycheck? Benito must pay 1% in Medicare taxes. How much money will be withheld from each paycheck? Social security taxes are 6% of your gross income. How much money will be withheld from each paycheck for social security taxes? Benito will also have to pay $287.95 in federal income tax. How much will Benito's paycheck be?
Step-by-step explanation:
annual salary (that means the income for a whole year) is
$36,000
1 year = 12 months.
twice a month = 2 times in a month
so, he gets 12×2 = 24 paychecks in a year.
so, the gross income per paycheck is
36,000 / 24 = $1,500
100% = $1,500
1% = 100%/100 = 1500/100 = $15
so, $15 will be withheld from each paycheck for Medicare taxes.
6% = 1%×6 = 15×6 = $90
so, $90 will be withheld from each paycheck for social security taxes.
and then there is the federal income tax of $287.95
so, he will actually get for each paycheck
1500 - 15 - 90 - 287.95 = $1,107.05
Which of the following is an example of the associative property of multiplication?
Answer:
The associative property of multiplication states that the product of three or more numbers remains the same regardless of how the numbers are grouped. For example, 3 × (5 × 6) = (3 × 5) × 6.
Step-by-step explanation:
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling
a number less than 12.
The probability of rolling a number less than 12 is 91.6%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
each case in the set is mutually exclusive with the others in the set, the probability that any one of its components will occur is equal to the sum of its component probabilities.
We can have the number 12, the probality will be 1/12
So the probability of rolling a number less than 12 is = (1 - probability of 12)
=1-1/12
=11/12
=0.916
Hence the probability of rolling a number less than 12 is 91.6%.
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Graph the polygon with the given vertices and its image after the given rotation about point A A(1, 4), B(6, 5), C(8, 2), D(3, 2) ; 90° counterclockwise
Check the picture below.
Select the function that represents a parabola with vertex at (2,–1) and a point (5,8) on its curve.
A)
ƒ(x) = (x – 2)2 – 1
B)
ƒ(x) = 2(x – 2)2 – 1
C)
ƒ(x) = 2(x + 2)2 – 1
D)
ƒ(x) = (x + 2)2 – 1
The equation of parabola is y = (x - 2)² - 1.
What is Vertex from of Parabola?We know that the standard form of the parabola is y=ax²+bx+c. Thus, the vertex form of a parabola is y = a(x-h)² + k.
Given:
Vertex (2, -1) and point (5, 8)
As, we know the vertex form of a parabola can be written as following
y = a(x - h)² + k ......(1)
Now, We are given that vertex is at (2,-1) and there is a point (5,8) on the curve.
i.e. h = 2 and k = -1,
x = 5 and y = 8
So, to find the value of a
y = a(x - h)² + k
8= a( 5- 2)² - 1
8= 9a - 1
9a= 9
a=1
Now, the equation of Parabola is
y = a(x - h)² + k
y = (x - 2)² - 1
Hence, the equation of parabola is y = (x - 2)² - 1.
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A card is drawn from a 52-card deck, the result is written down, and then the deck is shuffled. A card is drawn. What is the probability that the first card was a heart and the second card was not heart? Write your answer as a fraction.
The probability that the first card is a heart and the second one is not a heart is P = 0.19
How to get the probability?
A standard deck has 52 cards divided in 4 sets, such that each set has 13 cards.
The probability of randomly drawing a heart is equal to the quotient between the number of cards of the set heart (13) and the total number of cards (52), so we get:
p = 13/52
Now, the probability of not getting a heart is equal to the number of cards that are not hearts (3*13 = 39) and the total number of cards (now is 51 because we already took one).
q = 39/51
The joint probability is equal to the product between the two individual probabilities:
P = q*p = (13/52)*(39/51) = 0.19
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Help Please............
The statement that is true for the function, h is h(2) = 16
It is given that there is a function h
The range of function, h is [tex]1\leq h(x)\leq 25[/tex]
The domain of the function, h is [tex]-3 \leq x\leq 11[/tex]
And it is also given that h(8) = 19 and h(-2) = 2
Now,
The 1st option is h(-3) = -1
But the range of h is between 1 to 25, hence, this option is not true.
The 2nd option is h(8) = 21
But it is already given that h08) = 19, thus this option is not true.
The 3rd option is h(13) = 18
But the domain of h is between -3 and 11, So, this option is not true as well.
The fourth option is h(2) = 16
In this the values of range and domain are correct.
Thus, h(2) = 16.
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12. What is the sign of the following? Answer "positive," "negative," or "zero." (CONSIDER SLOPE OF TANGENT)
a. f'(2)
c. f'(4)
e. f'(7)
b. f'(x) in the interval (1, 3)
d. f'(x) in the interval (3,6)
f. f'(x) in the interval (6, 9)
g. f'(x) in the interval (9, 12)
Find the interval(s) where the function is increasing and the interval(s) where it is decreasing:
27. h(x):
37. h(x)=
15. f(x) = 3x +5 17. f(x) = 2x²+x+1 21. g(x)= x³ + 3x² +1
1
2x + 3
83. AVERAGE SPEED OF A HIGHWAY VEHICLE The average speed of a vehicle on a stretch of Route 134 between 6 A.M. and 10 A.M. on a
typical weekday is approximated by the function f(t) = 20t-40√t+50 (0 ≤t≤4)
where f(t) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6 A.M. Find the interval where fis
increasing and the interval where f is decreasing and interpret your results.
Based on the information, f(t) is increasing on [0,1) and decreasing on (1,4].
How to explain the functionIt should be noted that to find where the function is increasing and decreasing, we need to find the intervals where the derivative is positive or negative, respectively.
a. h'(x) = 3 > 0 for all x, so h(x) is increasing on (-∞, ∞).
b. h'(x) = 4x + 1 > 0 when x > -1/4, so h(x) is increasing on (-1/4, ∞). h'(x) = 4x + 1 < 0 when x < -1/4, so h(x) is decreasing on (-∞, -1/4).
c. f'(x) = 6x > 0 when x > 0, so f(x) is increasing on (0, ∞). f'(x) = 6x < 0 when x < 0, so f(x) is decreasing on (-∞, 0).
a. f(t) = 20t - 40√t + 50, f'(t) = 20 - 20/√t.
f'(t) > 0 when √t < 1, or t < 1. f'(t) < 0 when √t > 1, or t > 1.
Therefore, f(t) is increasing on [0,1) and decreasing on (1,4].
This means that during the first hour (from 6am to 7am), the average speed of the vehicle is increasing, while during the remaining 3 hours (from 7am to 10am), the average speed is decreasing.
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A client at a weight loss clinic lost 18.5 pounds (lb) in 4 weeks. If he loses the same amount of weight each day, how much weight does he lose per day? (Round your answer to 3 decimal places)
Answer:
0.007 pounds a day
Step-by-step explanation:
if he loses 18.5 pounds in 4 weeks then each week has 7 days so you divide 18.5 by 7 four times. HOPE THIS HELPS :)
What is the factored form of 8x24-27y?
o (8x8-27y2) (2x¹6+xy+3y¹)
○ (2x-3y²) (4x¹6 - 6x³y² +9y4)
16
16
o(2x8-3y2) (4x¹6 +6x8y² +9y4)
O (8x8-27y2) (2x¹6-6xy+3y4)
The factored form of 8x²⁴-27⁶ is (2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)
What is a factored form?Equations may be solved and x-intercepts can be found very quickly when a quadratic expression is in factored form and equal to 0. You may also find vertices and maximum and minimum values of the expression.
The four main methods of factoring are the Grouping method, Difference in Two Squares, Sum or Difference in Cubes, and Greatest Common Factor (GCF).
It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant. Examples of factors include ((5x + 2)(3x-1)) and ((2(x-1)(x+3)).
Given,
8x²⁴-27⁶
=(2x⁸)³-(3y²)³
=(2x⁸-3y²)((2x⁸)²+2x⁸×3y²+(3y²)²
=(2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)
Therefore, the factored form of 8x²⁴-27⁶ is (2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)
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Determine between which two consecutive integers does 7√2 lie?
Answer:
9 and 10
Step-by-step explanation:
To three decimal places
[tex]7 \sqrt{2} = 9.899[/tex]
So 7√2 is between 9 and 10 (closer to 10).
Which expression is equivalent to 4/5-1/2
Answer: 3/10
Step-by-step explanation:
4/5 is equal to 8/10 and 1/2 is equal to 5/10
then we have 8/10-5/10 which is 3/10
this is the answer since expressions can be a number
Find the integer closest to √42.3
Answer:
42 or 21.15?
not 100% sure but hope this helps
---------------------------------------------
Answer:
7
Step-by-step explanation:
the proper answer is 6.50384501660364
however, this isn't an integer.
to get it to become an integer, we round it up;
6.5 rounded up is 7
and therefore, the answer would be 7
hope this helps
1. A cinnamon toast recipe calls for 6 parts sugar to 1 part cinnamon. Place an X to indicate if each set of ingredients is proportional to the recipe. 4.5 tsp sugar and 0.75 cinnamon 9 tsp sugar and 1.5 tsp cinnamon 12 tsp sugar and 2 tsp cinnamon 15 tsp sugar and 3 tsp cinnamon proportional not proportional
Step-by-step explanation:
if they are proportional, then they must keep the original ratio of 6/1 of sugar to cinnamon.
X 4.5/0.75 = 6 = 6/1
X 9/1.5 = 6 = 6/1
X 12/2 = 6 = 6/1
15/3 = 5 and that is NOT 6/1 (not proportional)
Carmen is drawing a card from a standard deck of playing cards. Find each probability below.
Answer: How many cards are there tho?
Step-by-step explanation:
how to find intercepts from any given quadratic equation
Answer:
To find y-intercept: set x = 0 and solve for y. The point will be (0, y). To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).
Step-by-step explanation:
worksheet- triangle sum and exterior angle theorem, help pls!
The value of x in the given triangle is 110°.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given triangle,
∠A=65°, ∠B=90°, ∠C=80°, and ∠D=50°
To find the value of ∠E,
Use triangle ∠ABC, in which eqaute the sum of the angle of a triangle to 180°.
65+90+y=180
y=25
The remaining ∠C =80-25 = 55°
Use exterior angle theorem,
According to this, the sum of two interior angles is equal to an exterior angle.
x=50+55
x=105°
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consider functions f and g defined by the graph and table
The correct statements regarding the functions are given as follows:
Function g has a greater average rate of change on interval [0,2] than function f.Function g is exponential and eventually exceeds function f, which is linear.Function f has a greater y-intercept than function g.What are the classifications of the functions?Regarding the type of function, we have that:
f(x) is a linear function, as it's graph is a straight line.f(x) is an exponential function, as when x increases by one, y is multiplied by 1.5.The y-intercepts are the values of y for which x = 0, hence they are given as follows:
f(x) = 15.g(x) = 8.Hence function g(x) starts less than f(x), but it eventually exceeds function f(x), as it is exponential, meaning that it has a greater average rate of change.
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a(0.2)and b(6.6)are points on a straight line abcd ab=bc=cd work out the coordinates of d
Answer:
i also need help with this because 2,3
Step-by-step explanation: help wich always equals 5,3
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 60%pure antifreeze. The company wants to obtain 240 gallons of a mixture that contains 20% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?
The amount of gallons of water is 160 and gallons of the premium antifreeze solution that must be mixed is 80.
How to find the volume of water?Let y represent the volume of water
Hence,
Total volume equation :
x +y = 240 equation 1
Pure antifreeze volume:
0.60 = .20 × 240 gallons equation 2
Hence,
Equation 2
x = .20 × 240 /.60
x = 48 /.60
x = 80 (Pure antifreeze)
So,
y = 240 -80
y = 160 gallons of water
Therefore the volume of water is 160 gallons.
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Question
1
Graph the line passing through (-2, 4) whose slope is m =—1/4
Answer:
Step-by-step explanation:
these seem complicated, but just think about what they are asking. they are giving you a point and a slope to a line.
That gives you the hint to use the "point-slope" formula
if you don't have it memorized you might as well start trying to now. You'll need this over and over and over...
y-y1=m(x-x1)
so plug in the given info
y-4= (-1/4)(x-(-2))
y-4 = -1/4 (x +2)
y-4 = (-1/4)x -1/2
y = (-1/4)x + 7/2 this is the slope intercept formula. y = mx +b
we can now graph this line with the slope intercept formula.
note the graph does pass through (-2,4) and has a -1/4 slope :)
A giant tortoise can travel 0.15 miles in 1 hour. At this rate, how long would it take the tortoise to travel 1 mile
It would take the tortoise approximately ____
Answer:
6 [tex]\frac{2}{3}[/tex] Hours
Step-by-step explanation:
Distance = rate times time
Let t = time
1 = .15t Divide both sides by .15
6.666... = t The 6 is repeating so as a fraction it would be
6 [tex]\frac{2}{3}[/tex]
Andrew took the midterm exam a second time this week. Andrew earned a score of 72% last week, and calculated the absolute change in the scores to be an increase of 23 percentage points. Calculate Andrew’s score on the midterm this week.
Andrew's score on the midterms this week, based on his scores last week and the absolute change, is 95%.
How to find the midterm score?The Midterm score for this week increased by 23 percentage points over the midterm score for the last week. This increase in the midterm score was an absolute change and not a relative change.
As a result of this being an absolute change, the midterm score for Andrew this week would then be:
= Midterm score last week + absolute change in the score
= 72% + 23 percentage points
= 95%
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Hot Chocolate Sales and Outside Temperatures
$100 $213 $830 $679 $209 $189 $1,110 $456 $422 $235 $199
Sales ($).
Temperature
(°F)
a) Make a scatterplot of the data above. (2 points)
92° 88° 54° 62° 85° 16°
+
52⁰
65° 68°
89⁰
91°
Hot Chocolate Sales and Outside Temperatures:
(A) The scatter plot is shown below.
(B) The anomaly is located at (189, 16°F).
(C) A negative correlation exists.
(D) Sales are the dependent variable, and temperature is the independent variable.
What is Temperature?
The physical concept of temperature indicates in numerical form how hot or cold something is. A thermometer is used to determine temperature. Thermometers are calibrated using a variety of temperature scales, which historically defined various reference points and thermometric substances.
The following information is provided for hot chocolate sales and outside temperatures:
(Y) Sales Temperature (X)
100 92
213 88
830 54
679 62
209 85
189 16
1110 52
456 65
422 68
235 89
199 91
(A)
Attached below is the scatter plot.
(B)
A cluster is a group of points or values gathered in one location.
A cluster of three values between the temperatures of 80°F and 100°F may be seen on the scatter plot.
A value that differs significantly from the other values in a data set is referred to as an outlier. Either it's too little or it's too big.
In the given data collection, there is an outlier.
The anomalous value is (189, 16°F).
(C)
The scatter plot's points have a decreasing slope.
This suggests that the variables temperature and sales have a bad relationship.
There is a bad association as a result.
(D)
Dependent variables are variables that are being studied, or being kept an eye on for any changes while the other variables in the model are altered.
The variables that are changed to cause the dependent variable to vary proportionately are known as independent variables.
According to the outside temperature, the data in this case shows the sales of hot chocolate.
Sales are therefore the dependent variable, and temperature is the independent variable.
This is due to an increase in hot chocolate sales as the temperature drops.
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Tell whether the ratios form a proportion 12/22,18/33
The ratios of the given values 12/22,18/33 form a proportion because they all equals to 6/11.
How can we know that the values of 12/22,18/33 form a proportion?The concept that will be used is the concept of proportion. To know that the values whether they form a proportion, then, we will need to express them, in their lowest term.
12/22 can be expressed in its lowest term by dividing the denominator and the numerator by the factor of 2 givings us 6/11.
18/33 can be expressed in its lowest term by dividing the denominator and the numerator by the factor of 3 givings us 6/11.
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2. When x = 0, y = 3 and z = 5, what is the value
of 3xy³ + 2xy³z + xyz + xz?
The value of 3xy³ + 2xy³z + xyz + xz = 0
Substituting given value in an Equation:
To find the value of a given equation or expression replaces each variable with the given value.
For example, a = 1 and b = 3 then find 3a + 2b.
=> 3(1) + 2(3) = 3 + 6 = 9
Therefore, the value of 3a + 2b = 9
Multiplication with zeroMultiplying any number with zero will give zero i.e 3 × 0 = 0. No matter how large the number is when we multiply it by zero the result will be zero.
Here we have
x = 0, y = 3 and z = 5
We need to find the value of 3xy³ + 2xy³z + xyz + xz
Substitute given values in the given expression
=> 3(0)(y)³ + 2(0)y³z + (0)yz + (0)z [ x × 0 = 0 ]
=> 0 + 0 + 0 + 0
=> 0
Therefore,
The value of 3xy³ + 2xy³z + xyz + xz = 0
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the mean mass of 5 men is 76kg. the masses of 4 of the men are 72kg, 74kg, 75kg, and 81kg, what is the mass of the 5th? And
Answer:
78kg
Step-by-step explanation:
Let total mass be M.
mean=M÷5=76
M=380kg
mass of 4men is 72+74+75+81=302kg
mass of 5th man=380-302=78kg
write the expressions as the power of 2 (4*2^5)/(2^3*1/16)
The expressions (4×2⁵) / (2³ × 1/16) written as the power of 2 is 2⁸
How to write the expressions as the power of 2?
Given: (4×2⁵) / (2³ × 1/16)
In order to write this expression as the power of 2, we need to use some in indices law:
Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base": 5⁴ x 5³ = 5⁴⁺³ = 5⁷ and P⁴ x P⁶ = P¹⁰
Division law: To divide two variables or numbers with the same base, we need to subtract their powers and raise them to that base": 5¹⁰ ÷ 5³ = 5¹⁰⁻³ = 5⁷ and P⁸ ÷ P² = P⁸⁻² = P⁶
Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:
8⁻² = 1/8² and b⁻⁶ = 1/b⁶
Let's use the laws to create the given expressions as the power of 2:
(4×2⁵) / (2³ × 1/16) = (2²×2⁵) / (2³× 1/2⁴) Note: 4 = 2² and 16 = 2⁴
= (2²⁺⁵) /(2³⁺⁽⁻⁴⁾) Note: 1/2⁴ = 2⁻⁴ (reciprocal law)
= 2⁷ / 2⁻¹
= 2⁷⁻⁽⁻¹⁾ Division law
= 2⁸
Therefore, the expressions as the power of 2 is 2⁸
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The ratio of T-shirts to jumpers in Jacob's wardrobe is 8 : 7.
There are 24 T-shirts in his wardrobe. How many jumpers are there?
Answer:
24:23
Step-by-step explanation:
please help
A crate is 24cm by 18cm by 15cm . it is to be packed with boxes that are 8cm by 6cm by 5cm. What is the largest number of boxes that can fit into the crate .
Submit answer and show working out now !11
The largest number of boxes that can fit into the crate is 27.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
From the given data in the question,
The dimension of the crate is: 28 × 18 × 15
Volume of crate = 6480 cm³
And the dimensions of packs = 8 × 6 × 5
the volume of packs = 240 cm³
Then, the number of boxes that fit into the crate = 6480/240
= 27
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