Answer:
- 2
Step-by-step explanation:
the factors of a difference of square are
a² - b² = (a + b)(a - b)
(1 + [tex]\sqrt{3}[/tex] )(1 - [tex]\sqrt{3}[/tex] ) ← are the factors of a difference of squares , then
(1 + [tex]\sqrt{3}[/tex] )(1 - [tex]\sqrt{3}[/tex] )
= 1² - ([tex]\sqrt{3}[/tex] )²
= 1 - 3
= - 2
6. In a company, the number of men is 3.5 times more than the number of women. How many of the company's 108 employees are men?
Answer:
84
Step-by-Step Explanation:
simplify the expression: (3x10^8)(6x10^-4)
The answer is 18x10^4 using simple arithmetic calculations and exponential function.
What are arithmetic calculations?
Arithmetic calculations are mathematical operations that involve the addition, subtraction, multiplication, and division of real numbers. Arithmetic is used to solve problems and execute tasks in everyday life, and is an integral part of mathematics. It is also used to analyze data and solve equations. Arithmetic involves the use of numbers, symbols, and operations in order to solve problems. Examples of arithmetic operations include addition, subtraction, multiplication, division, and exponentiation. The order of operations is an important part of arithmetic, as it dictates which operations take precedence over others. Arithmetic is used in a variety of applications, such as in engineering, finance, education, and science. It can also be used to solve puzzles and games. Arithmetic calculations can be used to help people better understand the world around them, as well as to help them make better decisions in life.
Two exponential function having same base , then powers can be added or subtracted.
In given equation, base is of 10 and powers are 8 and -4.
now the power will be 4
and 3 and 6 get multiplied i.e. 18.
So, the answer is 18x10^4.
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a person leaves home and walks 4 miles west, then 5 miles southwest. how far from home is she? miles in what direction must she walk to head directly home? degrees north of east
The person is 8.325 miles far from her home and she should walk in the direction of 64.86° North Of East to head directly home .
In the question ,
from the figure ,
we see that point O is home of the person ,
it is given that person leaves the home and walks 4 miles west to point A , then 5 miles in south west direction to the point B .
So ,distance OA = 4 miles
AB = 5 miles .
In triangle OAB ,
angle OAB = 45+90 = 135°
Using Cosine Rule ,
OB² = OA² + AB² - 2*OA*AB*Cos(135)°
= 16 + 25 + 28.2843 = 69.2843
So ,OB = √69.2843 = 8.325 miles .
Now using Sine Rule ,
Sinθ/OA = Sin(135°)/OB
Sinθ = 4*Sin(135°)/8.324
Sinθ = 0.339792
So , θ = 19.86°
hence the direction from North of East is
= 45° + θ
= 45° + 19.86°
= 64.86° North Of East .
Therefore , the distance is 8.325 miles and the direction is 64.86° North Of East .
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Which of the following expressions is equal to
(sin 60°)(cos 30º) + (cos 60°)(sin 30°) ?
F. cos(60° -30°)
G. cos(60° +30°)
H. sin(60° -30°)
J. sin(60° +30°)
K. sin(60* 430")
+ °
2
The answer is cos 60° × cos 30° + sin 60° × sin 30° = √3/2.
Find the solution ?The fundamental guidelines and procedures to simplify any algebraic statement are as follows:By multiplying factors, remove any grouping symbols like brackets and parenthesis.
Simplify each term.
34+14
Combine fractions.
Combine the numerators over the common denominator.
3+14
Simplify the expression.
Add 3
and 1
44
Divide 4by 4
= 1.
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Sophia earns $16 per hour and worked 7.5 hours per day. She spent
$18 per workday on lunch. Sophia saves a quarter of her remaining
money in her savings per week.
A.
Write an expression representing the amount of money
Sophia put in her savings account at the end of the week.
B. How much money did she put in her savings?
The answers to both subparts are shown:
(A) The expression is: 4x = 714
(B) Money she put in her savings account each week: $178.5
What is an expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Let's assume she works 7 days a week.
Then 7.5 * 16 = $120 (1-day earning)
30 days: 120 * 30 = 840
$18 each day on lunch: 18 * 7 = $126
Remaining: 840 - 126 = $714
A quarter of $714: 714/4 = $178.5
(A) The expression will be:
4x = 714
(B) Money she put in her savings account each week:
4x = 714
x = 714/x
x = $178.5
Therefore, the answers to both subparts are shown:
(A) The expression is: 4x = 714
(B) Money she put in her savings account each week: $178.5
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for the 2015 general social survey, a comparison of females and males on the number of hours a day that the subject watched tv gave the following results.
Females = 504; mean 3.13
Males = 400; mean 2.87
-. set up the hyphoteses of a significance test to analyze wheter the population means differ for females and males
- conduct all parts of the significance test if df = 503 and standard error = 0.164 interpret the P-value and report the conclusion for a = 0.05
(a) The hypothesis to analyze is H₀ : [tex]\mu_{f} = \mu_{m}[/tex] v/s H₁ : [tex]\mu_{f} \neq \mu_{m}[/tex]
(b) the value of test stat is 1.585 and the p-value is 0.114 .
In the question ,
it is given that ,
the number of females is (n₁) = 504 and
mean (μ₁) = 3.13
the number of males is (n₂) = 400 and
mean (μ₂) = 2.87 .
Part(a) ,
the hypothesis to analyze whether the population means differ for females and males is ,
H₀ : [tex]\mu_{f} = \mu_{m}[/tex] v/s H₁ : [tex]\mu_{f} \neq \mu_{m}[/tex]
Part(b)
given that df = 503 and standard error (SE) = 0.164 and α = 0.05 .
So , the test statistic is :
t = (μ₁ - μ₂)/SE
= (3.13 - 2.87)/0.164
= 1.585
the p-value of the test can be calculated by :
P-Value = P(reject H)
= P(|t| > test stat)
= P(t > 1.585)
From the t table ,
we get the value as
= 0.114
the conclusion is p-value = 0.114 > 0.05 = alpha then we fail to reject the H₀ .
Therefore , the (a) hypothesis is H₀ : [tex]\mu_{f} = \mu_{m}[/tex] v/s H₁ : [tex]\mu_{f} \neq \mu_{m}[/tex] and
(b) the t stat is 1.585 and p value is 0.114 .
The given question is incomplete , the complete question is
For the 2015 general social survey, a comparison of females and males on the number of hours a day that the subject watched tv gave the following results.
Females = 504; mean 3.13
Males = 400; mean 2.87
(a) Set up the hypothesis of a significance test to analyze whether the population means differ for females and males .
(b) Conduct all parts of the significance test if df = 503 and standard error = 0.164 interpret the P-value and report the conclusion for a = 0.05 .
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The function h is defined by h (x) = 5x + 2 .
What is the value of h(8) ?
Responses
A) 30
B) 42
C) 38
D) 45
Answer:
Option B is the correct answer
Step-by-step explanation:
h(x) = 5x + 2, h(8)
h(8) = 5(8) + 2
h(8) = 40 + 2
h(8) = 42
Thus, The answer is 42
b.
5-50.
Use your new 30°-60°-90° and 45°-45°-90° triangle patterns to quickly find the lengths of
the missing sides
in
each of the triangles below. Do not use a calculator. Leave answers in exact form. Note: The triangles are not
necessarily drawn to scale.
a.
41
10
45°
8
4
30°
4
16
8
0
c.
d.
854
45°
9
30°
(2)
مع
60°
f.
60⁰
6
6
45°
The length of the sides of the special triangles, found using the relationship between the sides of the triangles are as follows;
(1) Length of the legs is 20 each
Length of the hypotenuse = 20·√2
(2) Length of the leg = 5
Length of the hypotenuse = 5·√2
5-50 a. Length of the leg is 10·√3
Length of the hypotenuse is 20
b. Length of the leg = 4
Length of the hypotenuse = 4·√2
c. Length of each leg = 8
d. Length of the leg = 9·√3
Length of the hypotenuse = 18
e. Length of the shorter leg = 4.5
Length of the longer leg = 4.5·√3
f. Length of the legs = 3·√2 each
5-51
Special triangles are the 30°, 60°, 90°, triangle, and the 45°, 45°, 90°, triangles.Please find attached the diagrams of special triangles, created with MS Word
What are triangles?
A triangle is a three sided polygon, that has a sum of interior angles of 180°
The lengths of the missing sides in the triangles found using the 30°–60°–90°, and 45°–45°–90°, triangle patterns are as follows;
In a 30°, 60°, 90° triangle, if the length of the shortest leg is x, the length of the hypotenuse is 2·x, and the length of the other leg is x·√3
In a 45°, 45°, 90° triangle, the length of the legs are the same, and the length of the hypotenuse is √2 multiplied by the length of one leg.
(1) The length of the legs are the same and equivalent to 20
The length of the hypotenuse side is 20·√2
(2) The length of the legs are the same and equivalent to 5
The length of the hypotenuse 5·√2
5-50 a. In the 30°, 60°, 90° triangle, the length of the adjacent, longer leg is 10·√3
The length of the hypotenuse side is 2·x
b. The triangle is a 45°, 45°, 90°, triangle
The length of the legs are 4 unit each
The length of the hypotenuse is 4·√2
c. The length of the hypotenuse in the 45°, 45°, 90° is 8·√2, therefore, the length of the legs are;
8 units each
d. The length of the shortest leg in the 30°, 60°, 90°, right triangle is 9, therefore, the length of the hypotenuse side is 2 × 9 = 18
The length of the longest leg is 9·√3
e. The length of the hypotenuse in the 30°, 60°, 90°, right triangle is 9 units, therefore, the length of the shortest leg is 4.5 units
The length of the longest leg is 4.5·√3
f. The length of the hypotenuse side of the 45°, 45°, 90°, right triangle is 6, therefore;
The length of the legs are 6/√2 = 3·√2
5-51
The dimensions of the side length of the special right triangles are;
In a 30°-60°-90° triangle, if the length of the shortest leg is x, then;
The length of the hypotenuse is 2·x
The length of the longer leg is x·√3
In a 45°-45°-90° right triangle, the length of the legs are the same, and the length of the hypotenuse is √2 multiplied by the length of one leg.
Please attached diagrams of the 45°, 45°, 90°, and the 30°, 60°, 90° triangles created with MS Word
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Which of the following is a equation of x-axis 1)y-0. 2)x-0. 3)x-0. 4)y-0
Answer:
none of the listed options
Step-by-step explanation:
the equation for x axis is y=0
Which of the following is a linear polynomial?
(A) x +5
(B) x2 +5
(C) x3 +5
(D) x4 +5
the correct answer is A cause × +5 is linear polynomial
Which scatter plot shows the best line of fit?
Multiple choice question.
A)
B)
C)
D)
Answer:
D
Step-by-step explanation:
The line of best fit is a line that represents the “average” between all of the points. It’s typically in the middle of all of the points. In this case, I’d go with D because 4 points lie on the line of best fit and the line trends sharply upwards, following the general direction of the points.
Rs. 85000 was exempted in the yearly income of a government service holder. If he paid tax Rs. 8850 in a year at the rate of 15%. What was his monthly income?
The monthly income of the government service holder is Rs. 12000
How to determine the monthly income?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Given that: Rs. 85000 was exempted in the yearly income of a government service holder. If he paid tax Rs. 8850 in a year at the rate of 15%.
Let P represent the yearly income. We can write that:
15% (P - 85000) = 8850
0.15(P - 85000) = 8850
0.15P - 12750 = 8850
0.15P = 8850 + 12750
0.15P = 21600
P = 21600/0.15
P = 144000
So the yearly income is Rs. 144000
Thus, the monthly income will be:
Rs. 144000 / 12 = Rs. 12000
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more than half of babies in the united states are born to unmarried parents. we want to know if this proportion is increasing. how do we define the population parameter of interest?
The current proportion of babies born to unmarried parents.
Given that,
In the United States, newborns born to unmarried parents make up more than half of all births. We are interested in learning if this ratio is rising. How should the population parameter be defined?
To find : Define the population parameter that interest ?
The present proportion of children born to unmarried parents should be our population parameter of interest since we want to know if the proportion is rising.
Our population parameter of interest should be the current proportion of children born to unmarried parents since we want to know if the proportion is increasing.
Therefore, the current percentage of children born to unmarried parents option (a) is right.
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A wire is used to anchor a 20-foot-tall pole. One end of the wire
is attached to the top of the pole. The other end is fastened to a
stake five feet away from the bottom of the pole. Find the length
of the wire.
The length of the wire attached to the pole is 20.62 feet
What is the length of the wire?The pole is perpendicular to the ground in the direction of the point where the wire is attached to the ground to form a right angle triangle.
A leg of the triangle is 20 feet(length of the pole from the surface of the ground to the top)
The other leg is5 feet(distance from the base of the pole to the point where the wire is attached to the ground)
The third side of the right angle triangle is the hypotenuse(length of the wire)
Applying Pythagoras theorem;
Hypotenuse² = Opposite² + Adjacent²
= 20 feet ² + 5 feet²
= 400 + 25
Hypotenuse² = 425
Find the square root of both sides
Hypotenuse = √425
= 20.6155
Approximately,
Hypotenuse = 20.62 feet
In conclusion, the hypotenuse side of the right angle triangle is 20.62 feet
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Which of the following statement is true ? a) X^2 + 5x -3 is a linear polynomial b) X^2+4x-1 is a binomial c) (x+1) is a monomial d) 5x^3 is a monomial
Answer:
d. [tex]5x^3[/tex] is a monomial
Step-by-step explanation:
⭐What is a monomial?
as "mono" means 1, monomial means an expression or equation that consists of 1 term onlyD is correct because the expression [tex]5x^3[/tex] consists of 1 term only.
⭐What is a linear polynomial?
a linear polynomial is an expression or equation that has a degree of 1⭐What is the degree of a polynomial?
the degree of a polynomial is the largest exponent found in the polynomialA is incorrect because the largest exponent in the expression [tex]x^2 + 5x -3[/tex] is 2, which makes expression A a quadratic polynomial.
⭐What is a binomial?
as "bi" means 2, a binomial is an expression or equation that consists of 2 terms onlyB is incorrect because the expression [tex]x^2 + 4x - 1[/tex] consists of 3 terms, not 2 terms. B is a trinomial.
C is incorrect because the expression [tex]x+1[/tex] consists of 2 terms, not 1 term. C is a binomial.
⭐if this response helped you, please mark it the "brainliest"!⭐
8. Fill in the boxes to estimate the
quotient.
8,521 48
8,500 ÷ blank = blank
The estimated quotient is 170.
What is the estimated quotient?The quotient is the result of a division operation.
A division operation involves the dividend divided by a divisor, which results in a quotient.
An estimated quotient is based on an approximation, which leaves out detailed calculations.
An approximated value is an amount or size closest to the true value. Approximations are determined by rounding off numbers, in this situation, the dividend, and the divisor.
8,521 ÷ 48
8,500 ÷ 50
= 170
Thus, approximating 8,521 to 8,500 and 48 to 50, the estimated quotient is 170.
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graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute. max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. how many minutes will it take graham and max to meet at the same altitude? a. 18.5 minutes b. 36 minutes c. 51.3 minutes d. 22 minutes
Answer: D:22,
14,040-12,500=1540.
1540/70 = 22
???????????????????????????
A recipe for pizza sauce calls for 11 cans of tomatoes and 44 teaspoons of oregano. How many teaspoons of oregano would you need for a single can of tomatoes?
Answer:
One can of tomatoes needs 4 teaspoons of oregano.
Step-by-step explanation:
[tex]\frac{11}{44}[/tex] = [tex]\frac{1}{x}[/tex] Cross multiply and solve for x
11x = 44 Divide both sides by 11
x = 4
One can of tomatoes needs 4 teaspoons of oregano.
Factor the polynomial
below completely:
14a-7
(Show work please)
a biologist wants to calculate the number of fish in a lake. on may 1 she catches a random sample of 60 fish, tags them, and releases them. on september 1 she catches a random sample of 70 fish and finds that 3 of them are tagged. to calculate the number of fish in the lake on may 1, she assumes that 25% of these fish are no longer in the lake on september 1 (because of death and emigrations), that 40% of the fish were not in the lake may 1 (because of births and immigrations), and that the number of untagged fish and tagged fish in the september 1 sample are representative of the total population. what does the biologist calculate for the number of fish in the lake on may 1?
The total number of fishes present in the lake on my 1 is 840.
Explain the term percentage of the number?A figure or ratio that may be stated as a percentage of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.The given data for the question-
42 fish were present in May out of the 70 fish that were caught in September, 40% of which were absent in May. Noting that the 25% death rate has no impact on the answer since both tagged and untagged fish die, the percentage the tagged fish inSeptember is equivalent to a percentage of tagged fish in May.
3/42 = 60/x
x = 60 *42 / 3
x = 840
Thus, the total number of fishes present in the lake on my 1 is 840.
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Passes through the point (-4, -3) and is perpendicular to the line -3x - 4y = 12.
Answer:
y= [tex]\frac{4}{3}[/tex] x+ [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
-3x-4y=12
1. First we need to get the equation in the form of y=mx+c to do this we add 3x to both sides and then divide it by -4 on each side to get
(add 3x to both sides) = -4y=3x+12
(divide each side by -4)= y= -[tex]\frac{3}{4}[/tex] x -3
2. to find the perpendicular gradient we find the reciprocal of the original gradient
the reciprocal of -[tex]\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex]
3. we can check this by multiplying them and seeing of we get -1
-[tex]\frac{3}{4}[/tex] x [tex]\frac{4}{3}[/tex] = = -1
4. we then sub in the gradient [tex]\frac{4}{3}[/tex] in y=mx+c this gives us
y= [tex]\frac{4}{3}[/tex]x +c
5. to find the value of c we substitute the coordinates into the equation to get ( we do this by expanding the brackets and getting c on it own)
-3= [tex]\frac{4}{3}[/tex](-4) +c
-3= -[tex]\frac{16}{3}[/tex] +c
[tex]\frac{7}{3}[/tex]=c
6. we sub [tex]\frac{7}{3}[/tex]=c back into y= [tex]\frac{4}{3}[/tex]x +c this gives us
y= [tex]\frac{4}{3}[/tex]x + [tex]\frac{7}{3}[/tex]
7. Therefore our final answer is
y= [tex]\frac{4}{3}[/tex]x + [tex]\frac{7}{3}[/tex]
Find the slope of each line. Tell whether the slop is Positive, Negative, Undefined or Zero
a manufacturer of transistors claims that its transistors will last an average of 1000 hours. to maintain this average, 25 resistors are tested each month. you may assume that the distribution of the lifetime of a transistor is normal. what conclusions can you draw from a sample that has a mean of 1010 and a standard deviation of 60?
Do not reject H(0). There is not sufficient evidence to a manufacturer of transistors claims that its transistors will last an average of different than 1000 hours. at 0.01 significance level.
In the given question, a manufacturer of transistors claims that its transistors will last an average of 1000 hours.
To maintain this average, 25 resistors are tested each month.
We may assume that the distribution of the lifetime of a transistor is normal.
We have to calculate a sample that has a mean of 1010 and a standard deviation of 60.
So let us consider
X : Life time of a transistor
So we have
N=25
x=1010
s=60
Since sample size n(25≤30) is small and population standard is unknown so we use t statistic for hypothesis testing.
Now our null and alternate hypotheses are given as:
H(0): μ=1000
H(1): μ≠1000 (two tailed test)
Under Null hypothesis our test statistic is;
t=(x-μ)/(s/√n)
t=(1010-1000)/(60/√25)
t=0.83
Critical Value:
t(α,(n-1))=t(0.01, 24)
t(α,(n-1))=2.80
We have given level of significance α=0.01 and also we find the t-score 0.83 and degree of freedom=24
p value
The Excel formula is used to calculate the p value is:
P value =2×(1- (t(24) > 0.83))
P value =2×(1-0.7926)
P value =2×0.2074
P value =0.4147
Since p value=0.42 greater than α=0.01 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected and we claims that its transistors will last an average of 1000 hours.
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How do you find 10% of a number?
Answer:
by dividing 10.
Step-by-step explanation:
100 percent if full. so to find ten percent, do 100 divided by 10.
(1,3) and (-3,-5) in linear equation
last year, 54% of business owners gave a holiday gift to their employees. a survey of business owners conducted this year indicates that 32 of them plan to provide a holiday gift to their employees. suppose the survey results are based on a sample of 80 business owners. (a) suppose the business owners in the sample did as they plan. compute the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year. find the value of the test statistic. (round your answer to two decimal places.)
The p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year is 0.0060 and the value of test statistic is - 2.51
54% of business owners gave a holiday gift to their employees. a survey of business owners conducted this year indicates that 32 of them plan to provide a holiday gift to their employees.
The survey results are based on a sample of 80 business owners
We need to find the value of test statistic.
Expected number = np = 32
80 x p = 32
p = 0.4
This is a left tailed test
test statistic is (p^ - p)/√(pq/n)
= (0.40 - 0.54)/√(.54 - (1 - 0.54) / 80)
= 0.14/√((0.54 - 0.46)/80)
= -2.51
p value = P(z < - 2.51)
= 0.00060366
= 0. 0060
Therefore, the p-value for a hypothesis test that can be used to determine if the proportion of business owners providing holiday gifts has decreased from last year is 0.0060 and the value of test statistic is - 2.51
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Max Says that the product 30 x 10 by 4 has exactly four zeros
Max Says that the product 30 x 10 by 4 has exactly four zeros is not true.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to check whether product 30 x 10 by 4 has exactly four zeros
firstly we have to multiply thirty with ten
Now multiply 30×10=300
Which has two zeros and now we have to divide it by 4
300/4
Three hundred by four
75
Seventy five.
Hence, Max Says that the product 30 x 10 by 4 has exactly four zeros is not true.
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If f(x) = (x ^ 2 - x + 1)/(x - 1) find f(- 1/2)
Answer:
[tex] \frac{7}{6} [/tex]
Find the Coefficient of [tex]{x}^{n}[/tex] In the following Expansion. ( See the attached Image )
given that |x| < 1
The Coefficient of xⁿ In the Expansion 1 / (1 + x + x²) is 1
What is coefficient?A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression.
It is typically a number, but it can also be any expression. They may also be referred to as parameters
The coefficient is usually the number in front of the variable represent by an letter.
For the given problem the given letter is x and the coefficient is 1, a coefficient of 1 is most times not written and hence we know the coefficient is 1
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