Step-by-step explanation:
Percentage means to be out of 100 . So, 20% is equivalent of being 20100 . That evaluates out to 0.20 . Removing the unnecessary 0 at the end gives us the decimal 0.2 , which is the correct answer.
In Alex's drawer she has 10 pairs of socks, 8 of which are white, and 9 tee shirts, 2 of which are white.
The probability of choosing a white pair of socks is
The probability of choosing a white tee shirt is
The probability of both being white is
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total socks= 10
White socks= 8
Total T- shirts= 9
White T- shirts = 2
Now, The probability of choosing a white pair of socks is
= 8/10
= 4/5
and, The probability of choosing a white tee shirt is
= 2/9
and, The probability of both being white is
= 4/5 x 2/9
= 8/45
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Is this how I do a sign analysis table? I’m not sure if I should include the x^2…
Answer:
I believe there is supposed to be something in the the corner box (Top left).
Step-by-step explanation:
Last week, the total weight of the members of a weight loss support group was 2,500 pounds. This week, it was 2,525 pounds. What percent heavier is the group now? %
The percent increase from 2,500 pounds this week to 2,525 pounds is 1% increase
How to find the percent increase of the weights?From the question, we have the following parameters that can be used in our computation:
Initial weight = 2500 pounds
New weight = 2525 pounds
The percentage increment is then calculated as
Percentage = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation
Percentage = (2525 - 2500)/2500 * 100%
Evaluate the difference
So, we have
Percentage = 25/2500 * 100%
Evaluate the quotient
So, we have
Percentage = 0.01 * 100%
Evaluate the product
So, we have
Percentage = 1%
Hence, the percent increase is 1% increase
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Choose from the drop-down menus to match the trigonometric expression with its value
The values that match the various trigonometric identity are;
1) sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀ = 1
2) cos 13 cos 47 + sin 13 sin 47 = 0.5
3) sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π = 0
How to solve Trigonometric Identities?Trigonometric identities are defined as the equations that involves the trigonometric functions that are true for every value of the variables involved.
1) We know that the trigonometric identity sin(A + B) is expressed as;
sin(A + B) = sinAcosB + cosAsinB
We are given;
sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀
Applying the trigonometric identity above, gives us;
sin(²/₅π + π/₁₀)
= sin(5π/10)
= sin(π/2)
= 1
2) We know that the trigonometric identity sin(A + B) is expressed as;
cos(A + B) = cosAcosB − sinAsinB.
We are given;
cos 13 cos 47 + sin 13 sin 47
Applying the trigonometric identity above, gives us;
cos(13 + 47)
= cos 60
= 0.5
3) We know that the trigonometric identity sin(A + B) is expressed as;
sin(A + B) = sinAcosB + cosAsinB
We are given;
sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π
Applying the trigonometric identity above, gives us;
sin(²/₅π + ⁸/₅π)
= sin(¹⁰/₅π)
= sin(2π)
= 0
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The operation * is defined as a*b=a+b-2ab
Evaluate 2* (3*5)
(2*3)*5
The value of 2*(3*5) = 68.
The value of (2*3)*5 = 68.
What is multiplication?
A mathematical formula that specifies the objects to be multiplied, known as a factor, produces a product. For instance, the product of 6 and 5 is 30.
Given: The operation * is defined as,
a*b = a + b - 2ab
We have to find the value of 2*(3*5) and (2*3)*5
First to find the value of 2*(3*5).
2*(3*5) = 2*(3 + 5 - 30) = 2*(-22) = 2 + (-22) - 2(-22)(2) = 68.
Now to find the value of (2*3)*5.
(2*3)*5 = (2 + 3 - 12)*5 = -7*5 = (-7) + 5 - 2(-7)(5) = -2 + 70 = 68.
Therefore, 2* (3*5) = 68 and (2*3)*5 = 68.
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1. How many games did each team play? The men played
Find the equation of the line
Answer:
[tex]y= \frac 12 x -3\\y=0.5x -3[/tex]
Depending if you can imput fractions, or decimal numbers.
Step-by-step explanation:
The slope can easily calculated as [tex]m=\frac{\Delta y}{\Delta x} = \frac {0-(-3)}{6-0} = \frac 36 = \frac12[/tex]
The y intercept can be easily read from the graph as and is -3
Can someone help me with this
Using the information from the given diagram, the measure of angle x (m ∠x) is 52°
Calculating the measures of anglesFrom the question, we are to determine the measure of angle x.
From the given diagram, we can write that
m ∠A + m ∠H + m ∠I = 180° (Sum of angle in a triangle)
Also,
m ∠K = m ∠I (Corresponding angles theorem)
∴ m ∠I = 62°
Thus,
x° + 66° + 62° = 180°
x° + 128° = 180°
x° = 180° - 128°
x° = 52°
Hence, the measure of ∠x 52°
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Need help with This also
Answer:
Step-by-step explanation:
8.5 inches divided by 2 = 4.25 inches which is the base of the triangle with a height of 5.8 inches. Area of that triangle is 1/2 x base x height = 1/2 x 4.25 inches x 5.8 inches = 12.325 inches squared. Two of the triangles make 1 full isoceles triangle= 2 x 12.325 inches squared = 24.65 inces squared. But there are 5 isoceles triangles in a pentagon, so 5 times 24.65 inches squared = 123.25 inches squared.
Can someone help me out with this math problem and weather it converges or diverges?
The given infinite series is divergent.
Given,
[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\frac{3n^2+n+1}{2n^2-1}}[/tex]
it is in the form,
[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\ a_n[/tex]
If the series is convergent then it satisfies,
i)[tex]b_{n+1}\ \leq\ b_n\ for\ all\ n[/tex]
ii)[tex]\lim_{n \to \infty} a_n =0[/tex]
if any of the above condition dissatisfies then the series is divergent
First check the 2nd condition,
[tex]\lim_{n \to \infty}\frac{3n^2+n+1}{2n^2-1}}\\\\= \lim_{n \to \infty}\frac{n^2(3+\frac{1}{n}+\frac{1}{n^2})}{n^2(2-\frac{1}{n^2})}}\\\\=\frac{3+0+0}{2-0}\\\\=\frac{3}{2}[/tex]
Here, [tex]\lim_{n \to \infty} a_n \neq 0[/tex]
Thus, the given series is divergent.
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589 in base five is
589 in base five is [tex]4324_{5}[/tex].
Given number:
589
converting to [tex]589_{5}[/tex].
⇒ 5|589
⇒ 5|117|4
⇒ 5|23|2
⇒ 5|4|3
⇒ 5|4|4
Now we write the last digit from last number to first that is,
= [tex]4324_{5}[/tex].
Hence 589 in base five is [tex]4324_{5}[/tex].
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what kind of transformation converts the graph of f(x)= -10(x-2)^2 into the graph of g(x)= -2(x-2)^2
The transformation that converts f(x) to g(x), f(x) is contraction by 5 units
What are transformations?Transformations are mathematical operations which change the shape and orientation of an object or function.
The types of transformations include
Dilation, Reflection, translationcontraction and rotationHow to find what kind of transformation converts f(x) to g(x)?Since we have the graph of f(x) = -10(x - 2)² into the graph of g(x)= -2(x - 2)².
We see that f(x) = -10(x - 2)²
= 5 × -2(x - 2)²
= 5g(x)
Since f(x) = 5g(x)
⇒g(x) = f(x)/5
So, we converts f(x) to g(x), f(x) is contraction by 5 units
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There are 8 kites in the sky, and 5 of those kites are striped. What fraction of
the kites are striped?
A. 6/8
B.5/8
C.5/13
D.4/8
What are the solutions of this quadratic equation?
2x2 + 16x − 8 = 0
Answer:
[tex]x= -4[/tex] + [tex]2\sqrt{5}[/tex] and [tex]x= -4 -2\sqrt{5}[/tex]
Step-by-step explanation:
[tex]ax^{2}[/tex] + [tex]bx[/tex] - [tex]c = 0[/tex]
For this equation: [tex]a = 2, b = 16, c = -8[/tex]
[tex]2x^{2}[/tex] + [tex]16x[/tex] - [tex]8 = 0[/tex]
Step 1: Use quadratic formula with [tex]a=2, b=16, c=-8[/tex]
[tex]x=\frac{-b + - \sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]x=\frac{-(16) + - \sqrt{16^{2}-4(2)(-8) } }{2(-2)}[/tex]
[tex]x=\frac{-16+- \sqrt{320} }{4}[/tex]
[tex]x= -4[/tex] + [tex]2\sqrt{5}[/tex] and [tex]x= -4 -2\sqrt{5}[/tex]
Hope this helps! :)
Which triangle congruence postulate would be used to prove the following triangles congruent?
1. AAS
2. SSS
3. SAS
4. HL
if the selling price for a shirt is $39.98 and the tax rate is 4.5% what is the sales tax
Answer:
8.25 % I got this answer right.
Simplify: 2cd3(c − d + 5)
Responses
A 2cd3 − 2c2d4 + 10c2d32 cd 3 − 2 c 2 d 4 + 10 c 2 d 3
B 2c2d3 − 2cd4 + 10cd32 c 2 d 3 − 2 cd 4 + 10 cd 3
C 2cd3 − 2cd3 + 10cd32 cd 3 − 2 cd 3 + 10 cd 3
D 2c2d3 − 2c2d4 + 10cd2
Simplification of the given expression 2cd³ (c - d +5) is given by
2c²d³ − 2cd⁴ + 10cd³.
As given in the question,
Given expression is equal to :
2cd³ (c - d +5)
Law of exponents for multiplication is given by:
mᵃ × mᵇ =mᵃ⁺ᵇ
Simplification of the given expression by open the parenthesis we have,
= 2cd³ × c - 2cd³ × d + 2cd³ × 5
Apply law of exponents for multiplication we get,
= 2c¹⁺¹d³ -2cd³⁺¹ + (2×5)cd³
= 2c²d³ -2cd⁴ + 10cd³
Therefore, simplification of the given expression 2cd³ (c - d +5) is given by 2c²d³ − 2cd⁴ + 10cd³.
The complete question is:
Simplify : 2cd³ (c - d +5)
a. 2cd³− 2c²d⁴ + 10c²d³
b. 2c²d³ − 2cd⁴ + 10cd³
c. 2cd³ − 2cd³ + 10cd³
d. 2c²d³− 2c²d⁴ + 10cd²
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(A) find the perimeter of triangle BCF, to the nearest hundredth
(B) find the area of triangle BCF
Perimeter of triangle FBC is 19.24 units
Area of triangle FBC is 100.62 square units
Given,
The triangle with vertices;
F(-3, 5)
B(3, 2)
C(1, -2)
We have to find the perimeter and area of the triangle;
Formula for getting distance from vertices;
D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
Here,
Length of FB; F(-3, 5), B(3, 2)D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(3 -(-3) )^{2}+(2 -5 )^{2} }[/tex]
= [tex]\sqrt{6^{2} +(-3)^{2} }[/tex]
= [tex]\sqrt{36+9}[/tex]
= √45
Length of BC; B(3, 2), C(1, -2)D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(1 -3 )^{2}+(-2-2)^{2} }[/tex]
= [tex]\sqrt{(-2)^{2} +(-4)^{2} }[/tex]
= [tex]\sqrt{4+16}[/tex]
= √20
Length of FC; F(-3, 5), C(1, -2)D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(1-(-3) )^{2}+(-2 -5)^{2} }[/tex]
= [tex]\sqrt{4^{2}+(-7)^{2} }[/tex]
= [tex]\sqrt{16+49}[/tex]
= √65
That is,
Length of side FB = √45 unitsLength of side BC = √20 unitsLength of side FC = √65 unitsNow,
Perimeter of triangle FBC = FB + BC + FC
= √45 + √20 + √65
= 19.24 units
Next,
Area of triangle FBC = 1/2 × BC × FB²
= 1/2 × √20 × √45²
= 100.62 square units.
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Write the expression as a power and evaluate it.
8•2^7
Answer:
1024
Step-by-step explanation:
8 times 2 to the 7th power
2 by the 7th power 128 times 8 1024
A scientist claims that 9% of viruses are airborne.
If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 533 viruses would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of airborne viruses in a sample of 533 viruses would differ is 0.0062.
How to calculate the probability?From the information, the scientist claims that 9% of viruses are airborne and the proportion of airborne viruses in a sample is 533 viruses.
The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.
The mean is 0.09 and the standard deviation is 0.012.
The probability will be:
= 1 - P[Z < (0.12 - 0.09/0.013)]
= 1 - P(Z < 2.5)
= 1 - 0.99379
= 0.0062
This shows the concept of solving probability regarding z values.
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Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the nth term. 5 th term is 0; 45 th term is -120
The first term of the sequence is 12 and the common difference is -3.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
Given that a formula for the nth term. 5th term is 0; 45th term is -120. The common difference is calculated as,
a₁ + d(5-1) = 0
a₁ + d(45 - 1) = -120
Solve the above equation,
a₁ + 4d = 0
-a₁ - 44d= +120
___________
-40d = 120
d = -3
The value of the first term is,
a₁ + 4d = 0
a₁ + 4 x -3 = 0
a₁ = 12
Therefore, the first term of the sequence is 12 and the common difference is -3.
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Please help me I NEED HELP
Answer:
Step-by-step explanation:
ABC = the draw of the square means that the angle is right
We can now say that the other two angles are acute because the sum of the interior angles of a triangle is 180 degrees
BCA = acute
CAB = acute
An employee makes $10.51 per hour but is getting a 3% increase. What is his new wage per hour to the nearest cent? What percentage of the original wage is his new wage?
The employee's new wage per hour is $10.83. The percentage increase of the original wage to his new wage is 3%.
What is a percentage increase?A percent increase means how much a percentage has gone up over time. To find this number, one would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease. The formula for percent increase equals to "Increase / original number (value) x 100".
Given data:
First, we find 3% of $10.51 to get new wage per hour
= 0.03$ * $10.51
= $0.32
Then, we add this increase to $10.51.
= $10.51 + $0.32
= $10.83
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I need help finding S please help fast
Answer:
s = 89°
Step-by-step explanation:
Exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.
[tex] \therefore[/tex]
[tex] \rm \implies (v + 1) \degree + (v - 28) \degree = (v + 32) \degree \\ \\ \rm \implies 2v - 27 \degree = (v + 32) \degree \\ \\ \rm \implies 2v -v = 32 \degree + 27 \degree \\ \\ \rm \implies v = 59 \degree [/tex]
Sum of angles in a straight line is equal to 180°
[tex] \therefore[/tex]
[tex]\rm \implies v + 32 \degree + s = 180 \degree \\ \\ \rm \implies 59 \degree + 32 \degree + s = 180 \degree \\ \\ \rm \implies s + 91 \degree = 180 \degree \\ \\ \rm \implies s = 180 \degree - 91 \degree \\ \\ \rm \implies s = 89 \degree[/tex]
solve the system of equations by the addition method
x-y= -2
x+y=4
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is }. (Type an ordered pair.)
B. There are infinitely many solutions. The solution set is {(x,y)}.
(Type an equation.)
C. There is no solution. The solution set is Ø.
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
You want to solve the system of equations x-y= -2; x+y=4 by the addition method.
Addition methodThe addition method seeks to eliminate one of the variables by adding the equations with appropriate multipliers so that one of the coefficients becomes zero.
Here, we observe that the coefficient of y in one equation is the opposite of that in the other equation. This means adding the two equations will cancel the y-terms:
(x -y) +(x +y) = (-2) +(4)
2x = 2 . . . . . . . . . . . . . . . . simplify; y-term is eliminated
x = 1 . . . . . . divide by 2
1 +y = 4 . . . . . . . substitute for x in the second equation
y = 3 . . . . . . . . . subtract 1
The solution is (x, y) = (1, 3).
2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?
A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds
The weight of Luna is 82 pounds , the correct option is (d) .
In the question ,
it is given that
Kira has three dogs Luna , Cooper and Daisy .
let the weight of cooper be c .
given Cooper weighs 25 pounds less than Daisy
which is c = daisy - 25
So , daisy = c + 25
and Luna weighs 20 pounds less than three times Cooper ,
which is Luna = 3c - 20
Given the combined weight is = 175 pounds
Cooper + Daisy + Luna = 175
c + c + 25 + 3c - 20 = 175
5c + 5 = 175
5c = 175 - 5
5c = 170
c = 170/5
c = 34
So, Luna = 3c - 20 = 102 - 20 = 82 pounds .
Therefore , The weight of Luna is 82 pounds .
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Jaden has a part-time job working for a landscaping company. He earns $25 for each lawn-mowing job, l, and $20 for each pulling-weeds job, w. This can be modeled by 25l+20w. Evaluate for l=4 and w=6 to find how much money Jaden will earn for 4 lawn-mowing jobs and 6 pulling-weeds jobs. Please helpppp
Answer:
220.
Step-by-step explanation:
If you plug in 4 for L and 6 for W, you are left with 25(4) + 20(6), which is equivalent to 100+120 = $220
Answer:
220
Step-by-step explanation:
(10-x)+(12-x)
how do you do this i can't do this at all.
Answer:
[tex]\sf -2x+22[/tex]Step-by-step explanation:
[tex]\sf (10-x)+(12-x)[/tex]
Simplify:-
[tex]\sf 10-x+12-x[/tex]
Combine like terms:-
[tex]\sf -x-x+10+12[/tex]
[tex]\sf (-x-x)=\bf -2x[/tex]
[tex]\sf (10+12)=\bf 22[/tex]
[tex]\sf -2x+22[/tex]
__________________Hope this helps!
Have a great day!
During December, Far Eas Services makes a credit sale of $2,800 (before sales taxes). The state sales tax rate is 6% and the local sales tax rate is 2.5%.
Record sales and sales tax payable.
The credit sale after state and local tax payable is 2562$.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
The credit sale before sales taxes = 2800$,
The rate of state sale tax = 6%,
And rate of local sale tax = 2.5%
The sale after state tax = 2800-2800×6/100=2800-168=2632,
The sale after local tax=2800-2800×2.5/100=2800-70=2730
The credit sale after state and local tax= 2800-168-70=2562.
The required credit sale =2562$.
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The average weight of a population of manatees is unknown. A random sample of manatees selected from the population yields a sample mean of x¯=880.3 pounds. Assume the sampling distribution of the mean has a standard deviation of σx¯=10.4 pounds. Use the Empirical Rule to construct a 68% confidence interval for the true population mean weight.
The confidence interval that we have for the population mean is given as [869.9 , 890.7]
How to solve for the confidence intervalThe confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.
We have the following data that we have to solve this problem with
The mean = x¯=880.3 pounds
The standard deviation = 10.4 pounds.
The confidence interval = 68%
To get the confidence interval for the true mean of the population weight we would have
mean ± standard deviation
880.3 ± 10.4
The interval would be written out as
880.3 - 10.4 and 880.3 + 10.4
the confidence interval =
[869.9 , 890.7]
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