I need this answer as soon as possible! 50 points!
[tex]20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5[/tex]
Answer:
[tex]800\sqrt{5}[/tex]
Step-by-step explanation:
Given: [tex]\large (20)^\text{$ \dfrac{5}{2} $}[/tex]
Properties of Exponents:
Rational Exponent Property: [tex]\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}[/tex]
a number raised to a fraction, can be converted to a radical. the numerator becomes the exponent, and the denominator becomes the index of the radical.Product of Powers Property:
when multiplying powers with the same base, add the exponents.1. Convert into a radical:
[tex]\sqrt[2]{20^5} \implies \sqrt{20^5}[/tex]
2. Simplify the expression:
[tex]\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}[/tex]
3. Evaluate the power:
[tex]20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}[/tex]
4. Multiply:
[tex](400\times2)\sqrt{5}\\\\\implies800\sqrt{5}[/tex]
Find the area to the nearesy square foot of the shaded region below, consisting of a square with a circle cut out of it.
Based on the calculations, the area of the shaded region is equal to 22 square foot.
How to calculate the area of the shaded region?By critically observing the geometric shapes, the area of the shaded region can be calculated by using this formula:
Area of shaded region = Area of square - Area of circle.
Note: The diameter of this circle is equal to the side length of the square because the circumference of this circle lies on the circumference of the square.
Radius = diameter/2 = 10/2 = 5 feet.
For the area of square, we have:
Area of square = S²
Area of square = 10²
Area of square = 100 square foot.
For the area of circle, we have:
Area of circle = πr²
Area of circle = 3.14 × 5²
Area of circle = 78.5 square foot.
Substituting the parameters into the formula, we have;
Area of shaded region = Area of square - Area of circle.
Area of shaded region = 100 - 78.5
Area of shaded region = 21.5 ≈ 22
Area of shaded region = 22 square foot.
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Complete Question:Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π.
Students are voting on the color of T-shirts to wear on their field trip. There are 160 students–65 boys and 95 girls–going on the field trip. A random sample of students is chosen. Surveying the random sample produced a representative sample of the population. Which was most likely true of the representative sample?
The representative sample contained all 160 students.
The representative sample contained more boys than girls.
The representative sample contained more girls than boys.
The representative sample contained an equal number of boys and girls.
Answer:
The representative sample contained more girls than boys.
Step-by-step explanation:
Since there is roughly 1.5x more girls than boys, the sample size will likely contain more girls than boys when chosen at random.
What’s the range of this graph?
A) all real numbers
B) all real numbers greater than or equal to 0
C) all real numbers greater than or equal to 1
D) all real numbers greater than or equal to 2
Option d is the correct answer. All real numbers are greater than or equal to 2.
What are domain and range?Domain of a function--The domain of the function is the set or collection of all the x-values for which the function is well defined.
Range of a function--The range of a function is the set of all the values which are attained by a function in its defined domain.
By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2). Hence, the range is: [2,∞).
Thus Option d is the correct answer. All real numbers are greater than or equal to 2.
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Simplify surd need an answer asap please
image is below, please help me fast i have 2 minutes left, thank you very much
Answer:
45
Step-by-step explanation:
1/3 of 90
= 1/3 * 90
= 90/3
= 30
Let the missing number be x.
2/3 of x
= 2/3 * x
= 2x/3
30 = 2x/3
Cross multiply,
2x = 30 * 3
2x = 90
x = 90/2
x = 45
Hence,
the missing number is 45.
If the total bill was $36 and I leave the waiter 9$, what percent is the tip
Answer:
25%
Step-by-step explanation:
percent = part/whole × 100%
percent = 9/36 × 100%
percent = 25%
Answer:
25%
Step-by-step explanation:
If you divide 36 by 9 you get 4. If you do the same for 100, and divide by four, you get 25. Therefore, 9 is 25% of 36.
Solve the system of
equation graphically, by
substitution, and by
elimination.
2x-5y = 34
y=3x-25
c) The ratio of boys to girls in a school is 4:5. There are 220 boys in the school. How many students attend the school?
Answer:
495Step-by-step explanation:
The ratio of boys to girls in a school is 4:5. There are 220 boys in the school. How many students attend the school?
find the number of girls
4 : 5 = 220 : x
x = 5 * 220 : 4
x = 275
sum boys and girls
220 + 275 =
495 (your answer)
check
4 : 5 = 220 : 275
4 : 5 = 4 : 5
the answer is good
Select the correct
What is the solution to this system of equations?
3x + y = 17
x + 2y = 49
O A.It has no solution.
OB. It has infinite solutions.
O C. It has a single solution: x = 15, y = 17.
OD. It has a single solution: x = -3, y = 26.
I need help please
A family purchases a light sphere to be used out on their patio. The diameter of the sphere is 20 in.
What is the volume of the light sphere?
Use 3.14 for pi.
Enter your answer, as a decimal, and round only your final answer to the nearest hundredth.
I have seen two different answers with 5 stars so I am confused on which person solved it correctly
Answer:
4,186.67 in³
Step-by-step explanation:
V = (4/3)πr³
V = (4/3)(3.14)(10 in)³
V = (4/3)(3.14)(1,000 in³)
V = 4,186.666667 in³
help and thank youu~
Answer:
Perimeter=150cm
Step-by-step explanation:
25cm×6=150cm
The Navy carrier, Mercy, is sailing in the Pacific Ocean. The ship is in the sea, 4,365 miles south of a city. On radar they notice a submarine is 7,390 miles away from them and north-west of their current position. What angle (off of a north-south line) do they need to travel to sail straight to the submarine?
The angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.
The Navy carrier, Mercy, is sailing in the Pacific Ocean. The ship is in the sea, 4,365 miles south of a city. On radar, they notice a submarine is 7,390 miles away from them and north-west of their current position.
Therefore, the angle at which the Carrier needs to move to reach the submarine is,
Cosθ = 4365/7390
θ = Cos⁻¹ (0.59)
θ = 53.843°
Hence, the angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.
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The graph below shows the altitude, in feet, of a model rocket t seconds after launch. During this time, the rocket
experiences three distinct modes of flight. Initially, the engine accelerates the rocket upward. The rocket then coasts
upward, is slowed by gravity, and eventually begins to fall. Last, a parachute opens and the rocket drifts smoothly
back to the ground.
1.000
200
20
Time after Launch (seconds)
When was the model rocket 600 feet above the ground?
4.5 seconds
7 seconds
7 and 9.5 seconds
O4.5 and 12 seconds
Deep spray
Answer:
D
Step-by-step explanation:
The model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.
What is graph?"It is a diagram that represents data in an organized manner."
What is altitude?"It is the height of the object above the surface of the ground."
For given question,
The graph shows the altitude, in feet, of a model rocket t seconds after launch.
From the graph we can observe that the model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.
Therefore, the model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.
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4.5% of what number is 46.116?
Answer:
47.1408
Step-by-step explanation:
They gave us the percentage of a number and wants us to find the whole
to do that we will use the following equation:
46.116*100/4.5 = 47.1408 is the number we are looking for.
What type of function is f(x) = 2x -14?
Exponential
Logarithmic
Polynomial
Rational
The function f(x) = 2x -14 is a polynomial function
How to determine the function type?The equation of the function is given as:
f(x) = 2x -14
A polynomial is represented as:
f(x) =ax^n + bx^(n - 1)....... + c
Where n is at least 1.
The function f(x) = 2x -14 is a polynomial with a degree of 1
Hence, the function f(x) = 2x -14 is a polynomial function
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I need to finish this, can someone please help!
Answer:
13
Step-by-step explanation:
a parallelogram has sides that are parallel to the opposite side. This means that y + 7 is going to be parallel to 20.
Two opposing sides of a parallelogram are parallel and equal
You know that the length of both of the sides is equivalent because the other set of opposing lines is also parallel (you can think of it as cutting off the line segment of y+7 and 20 at the same length. )
this means that we can set up the equation to find y as:
y + 7 = 20
then, you can proceed to find y by isolating it:
y + 7 = 20 ; so therefore
y + 7 = 20
- 7 -7
y = 13
y = 13
So, the value of y is 13
what is the of 6 in 46.97
What are the zeros of the quadratic function f(x) = 6x² - 24x + 1?
A.
[tex]x = - 2 + \sqrt{ \frac{1}{2} } or \: x = - 2 \: - \sqrt{ \frac{1}{2} } [/tex]
B.
[tex]x = 2 + \sqrt{ \frac{1}{2} } \: or \: x = 2 - \sqrt{ \frac{1}{2} } [/tex]
C.
[tex]x = - 2 + \sqrt{ \frac{23}{6} } \: or \: x = - 2 - \sqrt{ \frac{23}{6} } [/tex]
D.
[tex]x = 2 + \sqrt{ \frac{23}{6} } \: or \: x = 2 - \sqrt{ \frac{23}{6} } [/tex]
Answer:
D.
Step-by-step explanation:
Use Quadratic formula
x = [-b +- sqrt (b^2 - 4ac) ] / 2a with a = 6 b = -24 c = 1
to find
x = 2 ± sqrt (23/6)
The slope of a line is -1/5, and the y-intercept is 5. What is the equation of the line written in general form?
Answer:
y= -1/5x+5
STEP BY STEP EXPLAINATION:
m = slope = -1/5
c = y-intercept = 5
equation of a straight line:
y=mx+c
so.
y= -1/5x+5
What is the value of the next term in the geometric sequence graphed below?
OA. 4
B. 16
C. 8
OD. 32
SUBMIT
The value of the next term in the geometric sequence is 16
How to determine the next term?From the graph, we have the following highlights:
The graph is an exponential functiony multiplies by 2 as x increases by 1The means that:
Next term = Current term * 2
From the graph, we have:
Current term = 8
So, the equation becomes
Next term = 8 * 2
Evaluate
Next term = 16
Hence, the value of the next term in the geometric sequence is 16
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30% of the students in a class score an A on the last test. There are 50 students in the class. How many students scores an A on the test?
15
Step-by-step explanation:Percentages represent a proportion of a number. There are 2 ways to find a percent of a whole number.
Multiple of 10
Since 30% is a multiple of 10%, there is a shortcut we can use. We can find 10% and then multiply by 3 in order to find 30%. First, find 10% of 50. Like always, 10% of any number is that number divided by 10 (move the decimal 1 place to the left).
50/5 = 10So, 10% of 50 is 5.0.
Then, to find 30%, multiply 5 by 3.
5*3 = 1530% of 50 is 15.
Multiplication
The more consistent method includes multiplication, this can be used with any percentage. To use this method we need to convert 30% to a decimal. To convert any percentage to a decimal divide by 100 (move the decimal 2 places to the left).
30% / 100 = 0.30Now, we can multiply this decimal by the whole number, 50. This will give us our desired answer.
0.30*50 = 15So, this once again shows that 30% of 50 is 15.
A patient has been prescribed 1 gram (g) of Drug A. The stock dose is available in 250 milligram (mg) tablets. How many tablets would you administer per dose?
The patient would be administered 4 tablets per dose.
How do we use word problems to solve real-life problems?In mathematics, solving word problems involves a careful understanding of the content of the problem. This will enable the use of appropriate variables and data representation.
From the given information:
A patient has been prescribed = 1 gram of Drug A.A stock dose is available in = 250 mgFrom the standard conversion rate, we know that:
1 g = 1000 mgHere, to determine the number of dose to be administered, we have:
(x) /dose = 1000 mg/250 mg
x = 4 dose.
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An intravenous solution needs 2 liters (L) of glucose to be mixed with 7 units of blood. How much glucose (in liters) is needed for 30 units of blood
8.57 liters glucose (in liters) is needed for 30 units of blood.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
For 7 units of blood = 2 l of glucose needed.
Foe 1 units of blood, glucose needed = 2/7
For, 30 units of blood , glucose needed = 8.57 liters
Hence, 8.57 liters glucose (in liters) is needed for 30 units of blood.
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Determine the value of x please.
Figure and Answers choice below.
Answer:
B
Step-by-step explanation:
We can either use sine or cosine, I choose cosine but sine works the same. cos(angle) = adj/hyp. adj = cos(angle) x hyp. adj = cos(30)8, cos(30) = √3/2. √3/2 x 8 = 4√3
PLEASE HELP! PLEASE!!!!!!!
Using the equation of the proportional relationship:
Average rate of speed = 60
Time taken to go 300 miles = 5 hrs
Distance travelled in 2.5 hrs = 150 miles
What is a Equation of a Proportional Relationship?A equation of a proportional relationship models the relationship between two variables, x and y, that has a constant of k. It is expressed as y = kx.
Given the following:
Equation: d = 60t
d = distance in miles
t = time in hours
Average rate of speed for the bus = k = 60
Time (t) it would take to go 300 miles (d):
300 = 60(t)
300/60 = t
t = 5 hours
Distance (d) it would travel in 2.5 hours (t):
d = 60(2.5)
d = 150 miles
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a. Use the product rule to find the derivative of the given function.
b. Find the derivative by expanding the product first.
h(z)= (3-2²) (2³-2z+3)
Answer:
h'(z) = 2
Step-by-step explanation:
(b) First, let's expand everything so our equation is easier to look at.
h(z) = (3-4)(8-2z+3)
(-1)(-2z+11)
2z-11
Now, let's find the derivative:
h'(z) = 2
This data set represents the widths in yards of pieces of fabric used by a sewing group. What is the mean of this data set? {113, 14, 23, 12, 114}
Answer:
55.2 is the mean
Explanation:
Given data set: {113, 14, 23, 12, 114}
Mean = sum of the terms/number of terms
Mean = (113 + 14 + 23 + 12 + 114)/5
= (276)/5
= 55.2
Answer:
Mean = 55.2
Step-by-step explanation:
Given data set: 113, 14, 23, 12, 114
To find the mean of a data set, divide the sum of all data values by the total number of data values:
[tex]\large \begin{aligned}\sf Mean & = \sf\dfrac{sum\:of\:all\:data\:values}{total\:number\:of\:data\:values} \\\\\implies \sf Mean & = \sf \dfrac{113 + 14 + 23 + 12 + 114}{5}\\\\& = \sf \dfrac{276}{5}\\\\& = \sf 55.2\end{aligned}[/tex]
Find the value of x.
4x = 4
Hint! Remember the Multiplicative
Identity Property.
1.a = a
X = = [?]
Enter the number that belongs in the green box.
Enter
Answer:
x=1
Step-by-step explanation:
4x=4
(Linear equation)
Solved:-
Transpose 4 from LHS to RHS:
[tex] \rm = > x = \tt \cfrac{4}{4} [/tex]
[tex] \rm = > x = \tt1 [/tex]
raito 6 servings per platter
Answer: 6:1
Step-by-step explanation: