[tex]\sqrt{x^{10}} = x^5[/tex]
=====================================================
Explanation:
We simply take half of the exponent 10 to get 5. This applies to square roots only.
So the rule is [tex]\sqrt{a^b} = a^{b/2}[/tex]
A more general rule is
[tex]\sqrt[n]{a^b} = a^{b/n}[/tex]
If n = 2, then we're dealing with square roots like with this problem. In this case, a = x and b = 10.
Answer:
E
[tex] \sqrt{ {x}^{10} } \\ = \sqrt{ ({x}^{5} ) {}^{2} } \\ = {x}^{5} [/tex]
Write the equation of the line in slope-intercept form.
Answer:
y = 50x + 40
Step-by-step explanation:
2 points on the graph:
(0, 40) and (2, 140)
Slope:
m=(y2-y1)/(x2-x1)
m=(140 - 40)/(2 - 0)
m=(100)/2
m= 50
Slope-intercept:
y - y1 = m(x - x1)
y - 40 = 50(x - 0)
y - 40 = 50x
y = 50x + 40
She buys 12 bottles of tomato juice each bottle contains 3/4 cup of juice sheena also buys 12 bottles of orange juice each bottle contains 3 cups of orange juice
What is the mean of the numbers listed below ?
Answer: 47
Step-by-step explanation:
you find the middle of the number sequence and you see that 47 is in the middle making that the answer
Can someone answer the top two one and two for me please
Consider a random variable Z which has a standard normal distribution (mu = 0, sigma = 1). Choose which of the following values would be equivalent to the following probability:
P (Z > 0.54)
A. P(Z > 0.54.
B. P(Z < 0.54).
C. 1 - P(Z < - 0.54).
D. 1 - P(Z < 0.54).
Answer:
A. P ( Z > 0.54) = 0,7054
B. P ( Z < 0.54) = 0.2946
C.1) 1 - 0.2946 = 0.7054
D.1) 1 - 0.2946 = 0.7054
Step-by-step explanation:
A) P ( Z > 0.54) = 1 - P ( Z ≤ 0.54)
P ( Z ≤ 0.54) = 0,2946 from z-table
P ( Z > 0.54) = 1 - 0,2946
P ( Z > 0.54) = 0,7054
B) P ( Z < 0.54) = 0.2946
C) 1 - P ( Z < - 0,54)
1 - 0.2946 = 0.7054
D) 1 - P ( Z < 0,54)
1 - 0.2946 = 0.7054
If I can buy 4 calculators for $190, how much does one cost?
I would really appreciate if someone answered.
Answer:
47.50 per calculator
Step-by-step explanation:
Take the total cost and divide by the number of calculators to get the cost of one calculator
190/4 =47.50
birth weights in norway are normally distributed with a mean of 3570 g and a standard deviation of 500g. if the hospital officials plan to require special treatment for the lightest 3% of newborn babies, what birth weight seperates those requiring special treatment from those who do not
Answer:
2630 g
Step-by-step explanation:
From the given information:
Given that:
mean (μ) = 3750 g
Standard deviation (σ) = 500
Suppose the hospital officials demand special treatment with a percentage of lightest 3% (0.03) for newborn babies;
Then, the weight of birth that differentiates the babies that needed special treatment from those that do not can be computed as follows;
P(Z < z₁) = 0.03
Using the Excel Formula; =NORMSINV(0.03) = -1.88
z₁ = - 1.88
Using the test statistics z₁ formula:
[tex]z_1 = \dfrac{X-\mu}{\sigma}[/tex]
[tex]-1.88 = \dfrac{X-3570}{500}[/tex]
By cross multiply, we have:
-1.88 × 500 = X - 3570
-940 = X - 3570
-X = -3570 + 940
-X = -2630
X = 2630 g
Hence, 2630 g is the required weight of birth that differentiates the babies that needed special treatment from those that do not
pls help.. person with correct answer will be marked brainliest
Answer:
x = 43.4°
Step-by-step explanation:
when two straight line intersects, angles directly opposite of each other has the same value.
Which matrix equation can be used to solve the system?
(2x+ 5y = 15
X + 3y = 18
THE CORRECT OPTION IS A where the input data is correct
Answer:
option 3
Step-by-step explanation:
[tex]AX = B\\X = A^{-1}B\\\\A = \left[\begin{array}{CC}\\2&5\\1&3\end{array}\right]\\\\\\B =\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\X =\left[\begin{array}{C}\\x&y\end{array}\right][/tex]
[tex]det A = 1\\\\adj A = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right][/tex]
[tex]A^{-1} = \frac{1}{det A} \times Adj A[/tex]
[tex]= 1 \times \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\\\\\\= \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right][/tex]
Therefore,
[tex]X = A^{-1}B\\\\\\\left[\begin{array}{C}\\x&y\end{array}\right] = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\[/tex]
solve for x + 24 = -12
answer in the box
x equals_______
Answer:
x = -36
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 24 = -12
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 24 on both sides: x + 24 - 24 = -12 - 24[Subtraction] Simplify: x = -36Find the perimeter of the right triangle. If necessary, round to the nearest tenth.
a. 12 yd
b. 36 yd
54 yd
d. 144 yd
Please select the best answer from the choices provided
Answer:
B. 36 yd
Step-by-step explanation:
I calculated it logically
HELPPPP PLZZZZZzz HELLP FAST I NEED TO PASS
Answer:
✬ m∠Q= 105°➬➬➬➬➬➬➬➬
[tex]6x+5+(11x-5)+x=180^o[/tex]
[tex]18x=180[/tex]
[tex]x=10[/tex]
☄m∠Q=105°
❆❆❆❆❆❆❆❆❆❆❆❆
hope it helps....
have a great day!!
This is another problem for my math class
Solve the inequality below
X + 14 > 27
Answer:
x = 14+
Step-by-step explanation:
If 14 + 14 = 28
Then
28 > 27 is true.
What is the diameter of a hemisphere with a volume of 651 m^3, to the nearest tenth
of a meter?
Answer: 13.5 m, hope this helps :)
If the volume of the sphere is 651 m³. Then the diameter of the sphere will be 10.75 meters.
What is the volume of the sphere?If the given sphere is of radius r units, then its volume is given as:
V = 4/3 πr³ unit³
The volume of the sphere is 651 m³.
Then the diameter of the sphere will be
We know the formula in the form of diameter.
V = 1/6 πd³ unit³
Then we have
651 = 1/6 πd³
πd³ = 3906
d³ = 1243.31
d = 10.75 m
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what times what equals -4 and adds up to 3
Answer:
-4 and 1
Step-by-step explanation:
-4 times 1 equals -4 and then -4 plus 1 equals 3
The two numbers that satisfy the given conditions are 4 and -1. They multiply to -4 and add up to 3.
To find two numbers that satisfy the given conditions, we can set up a system of equations.
Let's assume the two numbers are represented by 'x' and 'y'. We know that their product is -4 and their sum is 3, so we can write the following equations:
xy = -4 (Equation 1)
x + y = 3 (Equation 2)
To solve this system of equations, we can use the substitution or elimination method. Let's use the substitution method.
From Equation 2, we can express y in terms of x: y = 3 - x.
Substituting this into Equation 1, we get:
x(3 - x) = -4
Expanding and rearranging the equation, we have:
3x - x² = -4
Rearranging again, we get a quadratic equation:
x² - 3x - 4 = 0
We can factor this equation:
(x - 4)(x + 1) = 0
Setting each factor to zero, we find two possible solutions for x:
x - 4 = 0 --> x = 4
x + 1 = 0 --> x = -1
Now, we can substitute these values of x back into Equation 2 to find the corresponding values of y:
For x = 4: y = 3 - 4 = -1
For x = -1: y = 3 - (-1) = 4
Therefore, the two numbers that satisfy the given conditions are 4 and -1. They multiply to -4 and add up to 3.
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what is the perimeter of this given figure
pahelp po. thank you
Answer:
14 units
Step-by-step explanation:
Side length of each square is 1 unit.
So, sum of the lengths of all the border edges = 14 units
Thus, the Perimeter of the figure = 14 units
Determine whether each expression below is always, sometimes, or never equivalent to sin x when 0° < x < 90° ? Can someone help me :(
Answer:
[tex](a)\ \cos(180 - x)[/tex] --- Never true
[tex](b)\ \cos(90 -x)[/tex] --- Always true
[tex](c)\ \cos(x)[/tex] ---- Sometimes true
[tex](d)\ \cos(2x)[/tex] ---- Sometimes true
Step-by-step explanation:
Given
[tex]\sin(x )[/tex]
Required
Determine if the following expression is always, sometimes of never true
[tex](a)\ \cos(180 - x)[/tex]
Expand using cosine rule
[tex]\cos(180 - x) = \cos(180)\cos(x) + \sin(180)\sin(x)[/tex]
[tex]\cos(180) = -1\ \ \sin(180) =0[/tex]
So, we have:
[tex]\cos(180 - x) = -1*\cos(x) + 0*\sin(x)[/tex]
[tex]\cos(180 - x) = -\cos(x) + 0[/tex]
[tex]\cos(180 - x) = -\cos(x)[/tex]
[tex]-\cos(x) \ne \sin(x)[/tex]
Hence: (a) is never true
[tex](b)\ \cos(90 -x)[/tex]
Expand using cosine rule
[tex]\cos(90 -x) = \cos(90)\cos(x) + \sin(90)\sin(x)[/tex]
[tex]\cos(90) = 0\ \ \sin(90) =1[/tex]
So, we have:
[tex]\cos(90 -x) = 0*\cos(x) + 1*\sin(x)[/tex]
[tex]\cos(90 -x) = 0+ \sin(x)[/tex]
[tex]\cos(90 -x) = \sin(x)[/tex]
Hence: (b) is always true
[tex](c)\ \cos(x)[/tex]
If
[tex]\sin(x) = \cos(x)[/tex]
Then:
[tex]x + x = 90[/tex]
[tex]2x = 90[/tex]
Divide both sides by 2
[tex]x = 45[/tex]
(c) is only true for [tex]x = 45[/tex]
Hence: (c) is sometimes true
[tex](d)\ \cos(2x)[/tex]
If
[tex]\sin(x) = \cos(2x)[/tex]
Then:
[tex]x + 2x = 90[/tex]
[tex]3x = 90[/tex]
Divide both sides by 2
[tex]x = 30[/tex]
(d) is only true for [tex]x = 30[/tex]
Hence: (d) is sometimes true
find the solution for x if |6x+8|=32
Answer:
X = 4
Step-by-step explanation:
6x + 8 = 32
6x = 32 - 8
6x = 24
x = 4
the solution is X = 4.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, we have,
6x + 8 = 32
6x = 32 - 8
6x = 24
x = 4
hence, the solution is x=4.
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I need help PLZZZ!!!
Subtract
-5-(-6)=
Answer:
1 is the answer
Step-by-step explanation:
-5-(-6) = x
-5 + 6 = x
1 = x
Answer:
s1: -5-(-6)
s2: -5 + 6. multiply minus with minus first
s3: +1. simply arthmatic.
Can anyone help me find the function for this trig graph ? i need a specific answer for the function , 50 pts
Answer:
y = 5 sin (2x) + 4
Step-by-step explanation:
this is sines function,
the amplitude is [9 - (-1)]/2 = 10/2 = 5
the period is 2πx/π = 2x
the x-axis of actual function is at y = 4
so, the function is :
y = 5 sin (2x) + 4
can someone help me i need help pls pls pls pls
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
[tex] \frac{2}{3} \times \frac{7}{4} \\ = \frac{2 \times 7}{3 \times 4} \\ = \frac{14}{12} \\ = \frac{7}{6} [/tex]
You'll get the answer as 7/6 which is equal to 1.16. 2/3 is equal to 0.66.
[tex]•°• \frac{7}{6} > \frac{2}{3} [/tex]
✐ So, the answer is ⇻ greater than 2/3.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
Find the length of the arc in terms of pi A 144° 10 AB = [?]
Answer:
Arc AB = 8π
Step-by-step explanation:
Length of arc = central angle/360 × 2πr
Where,
Central angle = measure of arc AB = 144° (central angle theorem)
r = radius = 10
Length of arc AB = 144/360 × 2 × π × 10
= 8π
Which of the following measures can have more than one value for a set of data?
© Median
- Mode
© Mean
© None of these
Answer:
mode
Step-by-step explanation:
All of the following are examples of essay types that colleges typically aska student to write except O A. essays about you. B. essays about a specific topic, C. essays about work experience, D. essays about your college choice.
Answer: C. essays about work experience
Step-by-step explanation: I would chose C because when you apply for a job you are asked to write and an essay on your work experience. But in college, you are no applying for a job.
How much material would it take to cover the sandbox?
Answer:
D.6,600 ft
Step-by-step explanation:
I hope it helps
What is the solution of log; (3x+2) = log: (4x-6)?
Answer:
x = 8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
Cancel the log from both sides and you'll get:
[tex]3x + 2 \: = 4x - 6 \: \\ 6 + 2 = 4x - 3x \: \\ x = 8[/tex]
Pizza Uno offers 2/3 of a small pizza for $3.50. Pizza Duo offers % of a small pizza for $4.20. How much does each charge for a whole small pizza?
Show your work and remember to answer the question.
Answer:
Pizza Uno offers $5.25 for a small pizza and Pizza Duo offers $5.60 for a small pizza.
Step-by-step explanation:
For Pizza Uno:
If 2/3 of a Pizza costs $3.50, divide it by 2.3.50 ÷ 2 = 1.75For each 1/3 it costs $1.75Multiply 1.75 by 3 to get a whole pizza.1.75 × 3 = 5.25For pizza Duo: (the "%" is actually 3/4)
If 3/4 of a pizza costs $4.20, divide it by each 1/4 you get (3).4.20 ÷ 3 = 1.40Each fourth (1/4) costs $1.40 eachMultiply 1.40 by 4 to get a whole pizza1.40 × 4 = 5.60prove that √3cosec20° - sec20° = 4
Answer:
LHS,
√3cosec20°-sec20°hope it helps.
stay safe healthy and happy.CAN SOMEONE ANSWER THIS?
tan ( 37 ) = x / 12
x = 12 * tan( 37 )
solve all of them for brianiest
Answer:
1.x= 3/-4-2 = x = 11/4
2.1.5x /1.5 = x
6/1.5=4
x=4