The numeric value of the expression sec²(54º) - 1, using a trigonometric identity, is given as follows:
tan²(54º) = 1.8944.
How to solve the expression using a trigonometric identity?Before applying the trigonometric identity, we have to define the secant and the tangent of an angle, as follows:
The secant of an angle is given by the division of one by the cosine of the angle.The tangent is given by the division of the sine of the angle by the cosine of the angle.The identity that exists between the squares of these measures is given as follows:
tan²(x) + 1 = sec²(x).
Hence, isolating the tangent:
tan²(x) = sec²(x) - 1.
In this problem, the expression is given as follows:
sec²(54º) - 1
Applying the identity, the expression is given as follows:
sec²(54º) - 1 = tan²(54º).
Using a calculator, the numeric value of the expression is given as follows:
tan²(54º) = 1.8944.
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Or the greenville tigers are having team shirts made. one option is to pay anthony's tees a $40 setup fee and then buy the shirts for $6 each. another option is to go to city printing, paying $20 for a setup fee and an additional $10 per shirt. the team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. what is the cost?
The total cost of the shirts that have same cost when x=5 is,
c=70
What is an equation?A mathematical equation is a formula that joins two expressions and expresses their equivalence using the equals symbol (=). The definitions of the word equation and its cognates in different languages may differ slightly.
The entire cost is c
c = 40 + 6x
c = 20 + 10x
The quantity of shirts is x.
Via utilizing one of the equations to solve for one of the variables and then substituting that variable's value into the other equation, you can solve by substitution.
40+6x=20+10x
4x=20
x=5
You would solve for c in the first equation in this problem.
40+6x where x=5 then,
c=70
Since it has already been solved for c, all that is left to do is swap out c with its equivalent in the second equation.
20+10x where x=5 then,
c=70
Therefore, the total cost of the shirts that have same cost is c=70 when x=5.
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611.2 times 0.0061 with steps please
well, there's no great mystery when it comes to getting a product from decimals. Now, we have 611.2 and 0.0061, let's for a second take off the decimal point and simply multipy 6112 times 00061
6112 * 00061 = 372832
ok....... hmmm now let's see 611.2 had 1 decimal, whilst 0.0061 had hmm 4 decimals, let's add them up, that's 1 + 4 = 5 decimals total from both amounts, that simply means that our 372832 needs to have 5 decimals as well, so that makes it 3.72832.
a recent survey showed that 9393 full-time employees out of a sample of 400400 did not use all of their vacation days last year. however, 118118 of those studied expressed a desire for more vacation time. based on this sample, if a full-time employee is chosen at random, what is the probability that he or she is content with the vacation allowance? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that he or she will be happy with the travel reimbursement will be 0.705.
The number of people who requested more vacation time indicates that they are plainly dissatisfied.
400 employees are satisfied with the vacation allowance. - The number of workers that requested greater vacation time.
Employees who are satisfied with their vacation pay are represented by the numbers 400 - 118 = 282.
The likelihood that he or she will be happy with the vacation allowance =
Employees that are happy with their vacation pay / Total number of employees
= 282 / 400 = 0.705.
Therefore, the likelihood that he or she will be happy with the vacation allowance = 70.5%
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Casey's Mail Manufacturing is a company that produces chain mail. Their most popular product is saw-cut metal links that hobbyists can use to make their own creations. The company recently spent $100 on advertising, which they hope to make back quickly. The wire used to produce one gram of links costs $2, but the finished links sell for $3 per gram. Eventually, the company will make back its investment and break even. How many grams of links must be sold?
In order to a breakpoint or the total cost = total investment company must need to sell 100 grams of links.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's suppose the number of links that are needed to solve for a breakpoint is x.
Cost of x number of links with the rate of $2/gram = 2x
Total cost = total selling
100 + 2x = 3x
3x - 2x = 100
x = $100
Hence "In order to break even point or the total cost = total investment company must need to sell 100 grams of links".
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I need the abswer to 20005+56258
76263
Step-by-step explanation:
[tex] \: \: \: 20005[/tex]
[tex] + 56258[/tex]
___________
[tex] = 76263[/tex]
A single bathc of your mother resipe for slalsa call for 3 tomatos. 1/4 cup cilantro,1/2 onion, and spices. you are having a party and need 5 batches of salsa how many cups of onions do you need?
To produce five constructive batches of salsa, 2.5 cups of onion will be needed.
What is unitary method of problem solving?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Given, the number of onions required to produce one batch = 0.5 cup(s)
∴ The number of onions required to produce five batches = 0.5×5
= 2.5 cup(s)
Thus, to produce five constructive batches of salsa, 2.5 cups of onion will be needed.
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Which of the following rules describes the function graphed below?
PLEASE ANSWER FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 asap!!!!!!!!!!!
The rule which describes the function graphed in the attached image as required to be identified is; Output = 8 - input.
Which rule represents the function graphed?It follows from the task content that the rule which is a representative of the function which is as graphed in the attached image is to be identified.
By observation, the relation which best describes the graph is; (7, 1), (6, 2), (5, 3).....
The inference which can therefore be drawn from the given graph is that;
The output value is the subtraction of the input value from 8 in each case.
Ultimately, the required rule which represents the function is; Output = 8 - input.
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The double number line shows that the distance from the start of a hiking trail to a cave entrance is 700\,\text{m}700m700, start text, m, end text.
Answer: 92
Step-by-step explanation:
If a, b, and c are positive prime numbers, in the equation a - b = c, either b or c must represent which number?
The value of prime numbers c in the equation is c = 2.
What is prime numbers?
Those greater than one are known as prime numbers. They simply have two variables, the number itself and factor 1.
We have given that a - b = c requires all of the integers to be positive prime numbers,
c can only have one outcome, which is 2.
[tex]e.g., 13 - 11 = 7 - 5 = 2.[/tex]
Hence in the given prime numbers c in the equation is c = 2.
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Write an equation of the line that passes through (1,6) and is parallel to the line shown.
Answer:
[tex]y=2x+4[/tex]
Step-by-step explanation:
The slope of the given line is [tex]\frac{-2-4}{-2-1}=2[/tex].
Parallel lines have the same slope, so the equation is:
[tex]y-6=2(x-1) \\ \\ y-6=2x-2 \\ \\ y=2x+4[/tex]
the coordinates of point are (-3,5). what are the coordinates of point B, which is a reflection of point A across the x-axis?
Answer:
Step-by-step explanation:
3 as the x axis and -5 for the y axis
An order of brown rice and quinoa weighs 17 pounds and costs $54.
Brown rice: $2.00 per pound
Quinoa: $4.50 per pound
How many pounds of brown rice and quinoa are in this order?
8 ounce of brown rice and 9 ounce quinoa sold.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Brown rice: $2.00 per pound
Quinoa: $4.50 per pound
let the brown rice sold x ounces
and, let the Quinoa sold be y ounces
So, the equations are:
x + y= 17
2x+ 4.5y= 54
2( 17- y) + 4.5y= 54
34 - 2y + 4.5y= 54
2.5y= 20
y= 20/2.5
y= 8 ounce
and, x= 17-8= 9 ounce
Hence, 8 ounce of brown rice and 9 ounce quinoa sold.
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You have 8,560 grams of a radioactive kind of rubidium. If its half-life is 15 minutes, how
much will be left after 45 minutes?
grams
Answer:
1,070 g
Step-by-step explanation:
Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 15 minutes. After 45 minutes, then, the amount of radioactive atoms is halved three times. Therefore:
1st half-life: 8,560 ÷ 2 = 4,280 g
2nd half-life: 4,280 ÷ 2 = 2,140 g
3rd half-life: 2,140 ÷ 2 = 1,070 g
Choose ALL answers that describe the quadrilateral UVWX if UV = 31,
VW = 67, WX = 45, XU = 56, m/U = 146°, m/V = 54°, m/W = 95°,
and m/X = 65°.
Parallelogram
□ Quadrilateral
Rectangle
Rhombus
Square
Trapezoid
The correct option ; Quadrilateral, has the given information describing quadrilateral UVWX.
What is meant by the term Quadrilateral? A polygon comprising four sides, 4 angles, and 4 vertices is called a quadrilateral.There are some aspects that all quadrilaterals share. These attributes are:There have been four of them.There have been four of them.360° is the summation of all interior angles.There have been two diagonals in them.For the given values in the question;
In the quadrilateral UVWX
Sides are;UV = 31,VW = 67, WX = 45, XU = 56, Angles are-m/U = 146°, m/V = 54°, m/W = 95°,and m/X = 65°.As, none of the sides are equal to other and none of the angles are equal to the other.
Thus, the this information shows the values are given for quadrilateral.
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5. Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? Explain your
reasoning.
Answer:
Andre is taller than Diego
Step-by-step explanation:
There are 100 cm in a meter. If we use this information and convert Diego's height to meters, we find that Diego is 1.65 m. This is a smaller number, and therefore, Diego is shorter than Andre.
1. 3x^2-7=31
2. 2x^2+18=0
3. 4x^2-26=-50
4. 2x^2+36=x^2
The quadratic equations are solved and answered below -
What is a equation?An equation is a mathematical statement showing the equivalence of two mathematical expressions. Example -
3x + 5 = 8
Given is -
3x² - 7 = 31
2x² + 18 = 0
4x² - 26 = - 50
2x² + 36 = x²
We have -
3x² - 7 = 31
3x² = 38
x² = 38/3
x² = 12.67
x = ±3.56
2x² + 18 = 0
2x² = - 18
x² = -9
x = ±3i
4x² - 26 = - 50
4x² = - 24
x² = -6
x = ±√6i
2x² + 36 = x²
x² = - 36
x = ±√6 i
Therefore, the quadratic equations are solved above.
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What is the sum of all the even numbers between 105 and 351?
What is the difference between the sum of all the even numbers between 305 and
609 and the sum of all the odd numbers between 304 and 608?
The sum of even numbers between 105 and 351 is 28,044 .
What is arithmetic progression ?An additive or arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.
Calculationeven numbers between 105 and 351
the series will start like
106 , 108 , 110 , .................................. , 346 , 348 , 350
this is a arithmetic progression
a = 106 d = 2 l = 350
we need to find n
350 = 106 + ( n - 1 ) 2
350 - 106 = (n -1 ) 2
244/2 = n -1
n = 123
now sum = 123/2 ( 106 + 350)
= 28,044
so the sum of even numbers between 105 and 351 is 28,044 .
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A certain airline charges a service fee of 7% for each plane ticket purchased. What is the total price the airline charges for a $320 plane ticket?
Answer: $342.40
Step-by-step explanation:
There are two ways you can solve this problem:
Simply turning the percentage to a decimal and multiplying it to the $320.
In the picture provided the method at the top represents you multiplying $320 x .07, You might be wondering “why .07 instead of 7%?” Well, if you were turning this number from a percent to a decimal you would shift the decimal point over to the left 2 times.
And so multiplying $320 x .07 = 22.4 or 22.40. Either way works but without the zero is the way you should write it. And you would add 22.4 to $320 and get $342.40.
Also in the picture provided I used the method of proportions.
Where the total is $320 in this case which you would put next to 100% as 100% means complete or the total. And you would put 7% above 100%. Then, proceed to cross multiply $320 by 7 and it will give you, 2240. Then, you divide it by 100. When you divide it you get 22.40. Then you would add it to $320 and get 342.40.
Editors preparing a report on the economy are trying to estimate the percentage of businesses that plan to hire
additional employees in the next 60 days. They are willing to accept a margin of error of 1% but want 95% confidence.
How many randomly selected employers will they need to contact?
n= (Round up to the nearest integer.)
The number of randomly selected employers that would have to be contacted is 9604
How to solve for the value of nThe confidence level is 95%
1 - 0.95 = 0.05
We have to get the z value at 0.05
0.05/2 = 0.025
Using the standard normal table, the critical value at 0.025 = 1.96
We have to define the probability as P = 50% = 0.5
we have to define q = 1 - 50% = 0.5
The formula that would be used to find the value of n is given as
[tex]n = pq\frac{Zc}{E} ^2[/tex]
These variables used are:
pq = variance of population
E = margin of error = 0.01
critical value = Zc = 1.96
[tex]n = 0.5*0.5 (\frac{1.96}{0.01})^2[/tex]
= 0.25 * 38416
= 9604
Hence the sample space is given as 9604
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EXPONENTS : PRODUCT RULE:
Simplify the expression 3 with the exponent 4, (Multiplying to), 3 with the exponent of 3.
The simplified expression is 2187.
Given expression:
expression 3 with the exponent 4 multiplying 3 with the exponent of 3.
= [tex]3^{4} *3^{3}[/tex]
we know that,
if base are equal exponents are added.
= [tex]3^{4+3}[/tex]
= [tex]3^{7}[/tex]
= 3*3*3*3*3*3*3
= 9*3*3*3*3*3
= 27*3*3*3*3
= 81*3*3*3
= 243*3*3
= 729*3
= 2187.
Therefore the simplified expression is 2187.
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You have eight marbles. all the marbles weigh the same, except for one, which is heavier than all the others. the marbles are otherwise indistinguishable. you may make no assumptions about how much heavier the heavy marble is. the task is to find the heavy marble by using a two-pan balance what is the minimum number of weighings required to identify the heavy marble?
A minimum of 3 weighings are required to identify the heavy marble out of 8 marbles.
As all the marbles weigh the same except one which is heavier, therefore firstly 8 marbles are divided into half. 4 marbles are placed in one pan while the other 4 are placed in another pan. In this two-pan balance, the pan which is lower than the other contains a heavier marble.
Now, the pan with heavier marble has 4 marbles which are again divided into half. 2 marbles are placed in each pan. Similarly, the pan with heavier marble goes down as compared to another pan with 2 marbles of the same weight. Now the final weighing is done by placing 1 marble in each pan out of 2 marbles taken from the pan which went down before as compared to another pan.
The pan with heavier marble will move down and thus with 3 weighings, a heavier marble is identified.
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 18
Blue 11
Green 8
Yellow 4
Purple 19
The probability that the next spin will land on red or green or purple is 75%
Given , A spinner is divided into five colored sections that are not of equal size
Color Frequency
Red 18
Blue 11
Green 8
Yellow 4
Purple 19
Total spin recorded = 18+11+8+4+19
=60
Let "A" be the event when spinner land on Red , "B" be the event when spinner land on Green and "C" be the event when spinner land on Purple
P(A) = 18/60 = 0.3
P(B) = 8/60 = 0.134
P(C) = 19/60 = 0.32
Probability that the next spin will land on red or green or purple will be P(A∪BC) = P(A) + P(B) + P(C)
P(A∪BC) = 0.3 + 0.134 + 0.32 =0.754
= 0.754 × 100 = 75%
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Time taken for a 3 litre bowl at a rate of 2 litre per minute
Thus, it takes 1.5 minutes {30 seconds} for filling a 3-litre bowl
2 Dora has solved the equation 4(x - 1) = 11
4(x - 1) = 11
4x41 = 11
4x = 52
x = 13
Dora is incorrect. Explain her mistake.
Dora put the x es
and did 4x11
11 and
Find the correct solution to 4(x − 1) = 11
I mark
Dora solved the equation.
She multiplies 4 inside the bracket. But she fails to know that 4× -1 = -4. Instead she multiplied that 4×-1 = -41. This is her first mistake.
In the second step, she shifted -41 to the right side in order to find the value of x. As -41 gets shifted to right side , -41 becomes +41 and added with +11 to get 52. which is totally a wrong method.
Step-by-step explanation:
Here is the exact method of solvation.
[tex]{ \blue{ \bold{4(x - 1) = 11}}}[/tex]
[tex]{ \blue{ \bold{4x - 4 = 11}}}[/tex]
[tex]{ \blue{ \bold{4x = 11 + 4}}}[/tex]
[tex]{ \blue{ \bold{4x = 15}}}[/tex]
[tex]{ \blue{ \boxed{ \red{ \sf{x = \frac{15}{4}}}}}} [/tex]
an environmental agency is analyzing soil samples from 50 farms for lead contamination. eight of the farms have dangerously high levels of lead. ten farms are randomly selected from the sample. using technology, how many ways could two contaminated farms and eight noncontaminated farms be chosen?
Number of ways , two contaminated and 8 non- contaminated farms be choosen is 3,304,845,180.
Permutation and Combination
Combination is a mathematical way to arranging the set of values randomly.
ⁿCᵣ = n! / r! (n-r)!
we have given that ,
total number of farms for lead contamination = 50
Number of farms have dangerously high level of lead = 8
so, number of non- containmated farms ( no high level of lead ) = 50-8 = 42
We have to find the number of ways to choose two contaminated farms and eight non- contaminated farms. Two containmated farms are selected from 8 containated farms and 8 non- contaminated farms are selected from 42 farms .
Number of ways for selecting two containmated farms = ⁸C₂ = 8!/2!×6! = 8×7/2 = 28
Number of ways for selecting eight non-containmated farms from 42 farms = ⁴²C₈
= 42! / 8! 34! = 42×41×---×35/8×7×----×1
= 118013185
The total number of ways to obtain 2 containmated farms and 8 non- contaminated farms in 10 farms selected is then product of number of ways to select the 2 containmated farms and number of ways to select 8 non-containmated farms .
= 118030185× 28 = 3,304,845,180
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Rewrite the following equation in slope-intercept form.
y − 8 = 2(x + 6)
A college student watched 15 movies in 8 1/3days. Find the students movie watching rate in movies per day
Answer: 1.8 movies per day.
Step-by-step explanation: 8 1/3=25/3. One day would be 3/25. This means that each day, a college students watched 3/25 of 8 movies. Do 3/25x15. This makes 1.8 movies watched per day.
f(x)=5+7x-9x^2+4^3 state the end behavior of f(x). Explain (x). Explain or show your reasoning.
The end behavior of given polynomial function f(x) = 5 + 7x - 9x^2 + 4^3,
as x → -∞, f(x) → -∞
as x → ∞, f(x) → -∞
In this question, we have been given a polynomial function
f(x) = 5 + 7x - 9x^2 + 4^3
We need to state the end behavior of f(x).
The graph of f(x) is as shown below.
We can observe that as x tends to -∞, f(x) → -∞
Also, as x → ∞, f(x) → -∞
We know that the end behavior of polynomial function is determined by the degree of the polynomial and the leading coefficient.
For given polynomial function, the degree of this polynomial is 2.
The leading coefficient is -9
We know that for polynomial function of even degree, the ends of the function graph point in the same direction.
Therefore, the end behavior of given polynomial function f(x) = 5 + 7x - 9x^2 + 4^3,
as x → -∞, f(x) → -∞
as x → ∞, f(x) → -∞
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solve for b: 84,250=b(1.008)120
Answer: 696.511
Step-by-step explanation:
84,250 = b(1.008)120
84250 = 120.96b
b = 696.511
3
3
Use exponent rules to explain why (√5)³ = √√5³.
Answer:
see image
Step-by-step explanation:
Use new exponent rules like:
A power raised to a power is the product of the powers. (power to a power, times the exponents)
and,
Square root is a half power. (Converting radicals to fractional exponents)
Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)
see image.
Here's the plan:
Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.
see image.
The proof of the equation (√5)³ = √(5³) is given below.
What is an exponent?Exponentiation is one of the mathematics operation.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
Given:
A radical equation,
(√5)³ = √(5³).
LHS = (√5)³
Simplifying,
(√5)³ = {(5[tex])^{1/2}[/tex]}³
= [tex]5^{3/2}[/tex]
= √(5³)
= RHS.
Therefore, (√5)³ = √(5³).
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The complete question:
Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.
