Answer:
8
Step-by-step explanation:
using \(a^2 = b^2 = c^2\) a= 6 c=10
Please Help! I'm lost, in a maze and I can't find my way out.
i need helpppppp i have no idea what im looking at lol
The correct answer is option B which is \(SinA = \dfrac{4}{5}\) , \(tanA = \dfrac{4}{3}\) ,\(SecA=\dfrac{5}{3}\),
\(CosA=\dfrac{3}{5}\),\(CotA=\dfrac{3}{4}\) and \(CscA=\dfrac{5}{4}\).
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
From the figure we can see that two sides are Ab = 15 cm and BC = 12 cm third side will be calculated by pythagorean theorem.
AC² = AB² - BC²
AC² = 15² - 12²
AC² = 81
AC = √81
AC = 9 cm
Now all the trigonometry identities are:-
\(SinA =\dfrac{BC}{AB}=\dfrac{12}{15}= \dfrac{4}{5}\) ,
\(tanA =\dfrac{BC}{AC}=\dfrac{12}{9}= \dfrac{4}{3}\) ,
\(SecA=\dfrac{AB}{AC}=\dfrac{15}{9}= \dfrac{5}{3}\),
\(CosA=\dfrac{AC}{AB}=\dfrac{9}{15}= \dfrac{3}{5}\),
\(CotA=\dfrac{AC}{BC}=\dfrac{9}{12}=}\dfrac{3}{4}\)
\(CscA=\dfrac{AB}{BC}=\dfrac{15}{12}= \dfrac{5}{4}\).
Therefore correct answer is option B which is \(SinA = \dfrac{4}{5}\) , \(tanA = \dfrac{4}{3}\) ,\(SecA=\dfrac{5}{3}\),\(CosA=\dfrac{3}{5}\),\(CotA=\dfrac{3}{4}\) and \(CscA=\dfrac{5}{4}\).
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17.
Which of the following are equiangular quadrilaterals?
a. parallelogram and rectangle
b. trapezoid and rhombus
c. square and rhombus
d. square and rectangle
e. none of these
Simplify (a÷b)³×(b÷c)×(c÷a)³ when a=3,b=a²,c=a³
Answer:
To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.
Substituting the values of a, b, and c:
a = 3
b = a² = 3² = 9
c = a³ = 3³ = 27
Now let's simplify the expression:
(a÷b)³×(b÷c)×(c÷a)³
(3÷9)³×(9÷27)×(27÷3)³
Simplifying each term:
(3÷9) = 1/3
(9÷27) = 1/3
(27÷3) = 9
Now we can substitute the simplified values back into the expression:
(1/3)³×(1/3)×9
Simplifying further:
(1/27)×(1/3)×9
1/9
Therefore, the simplified expression is 1/9.
Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 41 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.
(a) If the true mean is .9550 with a standard deviation of 0.0050, within what interval will 95 percent of the sample means fall? (Round your answers to 4 decimal places.)
We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).
To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.
The formula to calculate the margin of error is given by:
Margin of Error = Z * (Standard Deviation / √n)
Where:
Z is the critical value corresponding to the desired level of confidence
Standard Deviation is the standard deviation of the population
n is the sample size
Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.
The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.
Now we can calculate the margin of error:
Margin of Error = 1.96 * (0.0050 / √41)
Calculating this, we find:
Margin of Error ≈ 0.001624
To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:
Interval = True Mean ± Margin of Error
Interval = 0.9550 ± 0.001624
Calculating this, we find:
Interval ≈ (0.9534, 0.9566)
Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).
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Simplify.
−6x+86−32x−12+52x
Enter your answer in the box.
Do not use decimals in your answer.
Answer: 14x+74
Step-by-step explanation:
-6x+86-32x-12+52x=14x+74
-6x+86-32x-12+52x
=-6x-32x+52x+86-12
=14x+86-12
=14x+74
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The final expression after simplifying is 14x + 74.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
3x + 4 = 3 is an expression.
3 + 4x - 5 is an expression.
We have,
-6x + 86 - 32x - 12 + 52x
Add like terms.
-6x - 32x + 52x = 14x
Now,
14x + 86 - 12
14x + 74
Thus,
The final expression after simplifying is 14x + 74.
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A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.
A graph for p of x is a downward open parabola with its vertex at (5, 725) and passes through the points (negative 10, 0), and (20, 0).
Use the graph to complete each statement about this situation.
The maximum profit the florist will earn from selling celebration bouquets is $.
The florist will break-even after one-dollar decreases.
The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is ( , ).
Answer:
The maximum profit the florist will earn from selling celebration bouquets is $725.
The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.
The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.
Step-by-step explanation:
simplify √([2m5z6]/[ xy])
The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).
To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:
Simplify the numerator:
√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)
= √2m√5z√6
Simplify the denominator:
√(xy) = √(x) * √(y)
Combine the numerator and denominator:
√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)
Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).
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1. We want to know how much money Houston people would like to spend on
restaurants every month. So we randomly find 500 volunteers to do a survey
questionnaire. Identify the population.
A. 500 volunteers
B. Houston people
Help me please I beg of you
A,B,D,G,K what comes after
6) 3x2 + 10X - 8We have to find the vertex
Given:
\(3x^2+10x-8\)To find the vertex, use the vertex formula below:
\(y\text{ = }a(x-h)^2+k\)Where the vertex is: (h, k)
Thus, we have:
\(y=3x^2+10x-8\)\(\begin{gathered} y+8=3x^2+10-8+8 \\ \\ y+8=3x^2+10 \end{gathered}\)Factorize:
\(undefined\)This year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year
Answer:
4.28%
Step-by-step explanation:
We Know
Last year you earned $72,400
This year you earned $75,500
What was the rate of change in your earnings since last year?
We Take
(75,500 ÷ 72,400) x 100 ≈ 104.28%
Then We Take
104.28 - 100 = 4.28%
So, the earning increased by about 4.28%.
I rent a gym for $150 for 30 students. Another time I rent the gym for $350 for 70 students. What is my rate per student?
Answer:
The rate is 5 dollars per student.
Step-by-step explanation:
The rate per student can be found with \(\frac{dollars}{student}\):
\(\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}\)
The rate is 5 dollars per student.
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Which equation can be used to solve for x xx in the following diagram? Choose 1 answer: (Choice A) A ( 5 x + 30 ) − 5 x = 90 (5x+30)−5x=90left parenthesis, 5, x, plus, 30, right parenthesis, minus, 5, x, equals, 90 (Choice B) B ( 5 x + 30 ) + 5 x = 180 (5x+30)+5x=180left parenthesis, 5, x, plus, 30, right parenthesis, plus, 5, x, equals, 180 (Choice C) C ( 5 x + 30 ) + 5 x = 90 (5x+30)+5x=90left parenthesis, 5, x, plus, 30, right parenthesis, plus, 5, x, equals, 90 (Choice D) D 5 x = ( 5 x + 30 ) 5x=(5x+30)
Answer: answer is C
Step-by-step explanation:
for find x
(5x+30)+5x=90
5x+30+5x=90 add like terms
after,
10x+30=90
10x+30-30=90-30
10x/10=60/10
x = 6
to obtain answer as C
it mean
(5x+30)+5x=90
(5(6)+30)+5(6)=90 we know x=6 so add 6 to x and multiply and obtain answer is correct!
30+30+30=90
Suppose that the length of a confidence interval is 0.06 when the sample size is 400. Determine how the sample size must change to decrease the length of the confidence interval to 0.03 (Use decimal notation. Give your answer as a whole number:) new sample size:
We use Z-Distribution for large sample sizes, The reduced sample size is 200.
What do you mean by probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
What do you mean by Z-distribution?A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.
confidence interval = 0.06
Sample size= 400
new interval of confidence = 0.03
new sample size = 400/0.06 * 0.03
=200
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what is 2x to the power of 2
helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
2x^2 = (2 x 2) x (2 x 2)
= 4 x 4
= 16
I hope this helps you
Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows. Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4 What was Brooke’s error? She found the incorrect slope in step 1. She mixed up the x- and y-coordinates when she plugged in the point in step 2. She found the incorrect y-intercept in step 2. She mixed up the slope and y-intercept when she wrote the equation in step 3.
B. The correct answer is b. I just took it
Answer:
B.
Step-by-step explanation:
I need help with this if do thank you a lot
Applying the inscribed angle theorem, the measures are:
a. m<CBD = 70° b. m<A = 50° c. m<CBD = 22
What is the Inscribed Angle Theorem?The inscribed angle theorem states that the measure of an inscribed angle is half of the measure of the arc it intercepts in a circle. Also, the measure of a central angle is the same as that of the measure of the intercepted arc.
a. m<A = 35°
measure of arc CD = 2(35) [inscribed angle theorem]
measure of arc CD = 70°
m<CBD = m(CD) =
m<CBD = 70°
b. m<CBD = 100°
m(CD) = 100°
m<A = 1/2(100) [inscribed angle theorem]
m<A = 50°
c. m<A = x
m<CBD = 22
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which number line shows the solution to x + 8 > 15
7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The given inequality is:
x + 8 > 15
Subtracting 8 on both sides of the equation:
x + 8 - 8 > 15 - 8
x > 7
Here, 7 is not included and hence it is depicted using an open dot.
Hence, option B is the correct answer.
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Solve for x. Round to the nearest tenth.
27
X=
X
10
Answer:270
Step-by-step explanation:
27 x 10 = 270
A block of wood has a density of 0.6g/cm^3 and a volume of 1.2cm^3.What is the mass of the block of wood?
Answer:
Below
Step-by-step explanation:
You can use this formula to calculate the mass of an object
Mass = Volume x Density
Plugging everything in....
Mass = ( 1.2cm^3 ) ( 0.6g/cm^2 )
= 0.72 g
Hope this helps!
Can someone please help me with this math problem, ASAP?
The equation rewritten as a function of x is
\(y \ln \left(-2 x+x^2+2 y \right)=\ln (x)\)
What is a mathematical function?Generally, In the field of mathematics, an assignment of one element from set Y to each and every element in set X is the definition of a function. This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.
Historically, functions have been seen as an idealization of the way in which one variable relies on another variable. Wikipedia
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Which graph represents a line with a slope of and a y-intercept equal to that of the line y = x – 2? A coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2) and (2, 1). A coordinate plane with a line passing through (negative 3, 0) and (0, 2). A coordinate plane with a line passing through (0, 2) and (2, negative 1). A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2). Mark this and return
The first option is the correct one for the line y = x - 2:
" coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2)"
Which is the graph of the line?Here we want to identify the graph of the linear equation:
y = x - 2
First, notice that when we evaluate this in x = 0 we get the y-intercept:
y = 0 - 2
y = -2
Then the y-intercept there is (0, -2)
Also, evaluating the linear equation in x = -2, then we will get:
y = -2 - 2
y = -4
So we have the point (-2, -4)
Then the correct option is the first one:
" coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2)"
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Write the rule that should be applied to a list of inputs that are fractions with a denominator of 2 to change them to whole numbers. Provide a reason for your answer.
To change fractions with a denominator of 2 to whole numbers, multiply each fraction by 2, because multiplying both the numerator and denominator by the same number results in an equivalent fraction with a denominator of 1, effectively converting it to a whole number.
To change a list of inputs that are fractions with a denominator of 2 to whole numbers, we can apply the rule of multiplying each fraction by 2. The reason for this is based on the fundamental concept of equivalent fractions.
When we multiply a fraction by a certain number, we are essentially multiplying both the numerator and denominator by that number. In this case, since we want to convert fractions with a denominator of 2 to whole numbers, we need to find a number that, when multiplied by 2, results in a denominator of 1.
By multiplying each fraction in the list by 2, the denominator will become 1 (2 multiplied by 2 is 4, which simplifies to 1).
Since any number divided by 1 is equal to that number itself, the fractions will be converted to whole numbers.
For example, let's consider the fraction 3/2.
When we multiply it by 2, we get (3/2) \(\times\) 2 = (32)/(22) = 6/4.
Simplifying 6/4 gives us 3/2 again, but now the denominator is 1.
Therefore, by applying the rule of multiplying each fraction by 2, we can convert a list of fractions with a denominator of 2 to whole numbers.
This rule works because it effectively cancels out the denominator of 2, resulting in equivalent fractions with a denominator of 1, which are whole numbers.
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Camp Activities During the 6-hour session at day camp, Roland participated in boating, hiking, and lunch. The rest of the session was free time. How much time did Roland spend on the three activities? How much free time did he have?
a) Using addition operations, Roland spent 5¹/4 hours on the three activities that he participated in.
b) Based on subtraction operation, Roland enjoyed ³/₄ hours of free time.
What are mathematical operations?The four basic mathematical operations have been identified as addition, subtraction, division, and multiplication.
For the total time that Roland spent on the three camp activities he participated in, we use addition operation to determine it.
The addition operation involves two or more addends added to get the sum.
Lastly, since Roland spent 6 hours at the camp, we can use the subtraction operation to determine that he had ³/₄ hours of free time.
Roland's Participation:Camp Activities Time Allocated
Boating 1¹/₂ hours
Hiking 2¹/2 hours
Lunch 1¹/4 hours
Total 5¹/4 hours
Free time = ³/₄ hours (6 - 5¹/4)
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Question Completion:Camp Activities Time Allocated
Swimming 3/4 hours
Boating 1¹/₂ hours
Crafts 1³/₄ hours
Hiking 2¹/2 hours
Lunch 1¹/4 hours
find the common ratio of the geometric sequence 4,3,9/4
Answer:
3/4
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
3/4
Check with the third and second terms
9/4 ÷3
9/4 *1/3= 3/4
The common ratio is 3/4
For any unit vectors v and w, find the dot products (actual numbers) of
(a) v and -v (b) v + w and v – w (c) v – 2w and v + 2w
a) The dot product of v and -v is -1.
b) The dot product of v + w and v – w is 2v.w
c) The dot product of v – 2w and v + 2w is 4||w||^2 - 4v.w
(a) For any unit vector v, the dot product of v and -v can be found as follows:
v · -v = ||v||||-v||cos(θ) = ||v||||v||cos(180°) = -||v||^2 = -1, where ||v|| represents the magnitude of the vector v and θ is the angle between the vectors.
Since v and -v are unit vectors, their magnitudes are equal to 1, so ||v||^2 = 1. Thus, the dot product of v and -v is -1.
(b) For any unit vectors v and w, the dot product of v + w and v – w can be found as follows:
(v + w) · (v – w) = ||v + w||||v – w||cos(θ) = (||v||||v|| + 2v · w + ||w||||w||)cos(θ) = 2v · w
where θ is the angle between the vectors v + w and v – w, and v · w is the dot product of v and w.
(c) For any unit vectors v and w, the dot product of v – 2w and v + 2w can be found as follows:
(v – 2w) · (v + 2w) = ||v – 2w||||v + 2w||cos(θ) = (||v||||v|| + 4||w||||w|| - 4v · w)cos(θ) = 4||w||^2 - 4v · w
where θ is the angle between the vectors v – 2w and v + 2w, and v · w is the dot product of v and w.
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Help me plz plz help me with this question
Answer:
6 97/100 bags
Step-by-step explanation:
4 1/10 ⋅ 1 7/10 = ?
41/10 ⋅ 17/10 = 697/100
697/100 = 6 97/100
6 97/100 bags
Answer:
697/100 bags
or
6 97/100 bags
Step-by-step explanation:
it is fractions. just plain and simple.
when you eat a pizza slice, it is usually one of 8 slices that make the whole pizza. 1/8 or one 8th. meaning that the whole thing is 8/8 or eight 8ths.
the same for 10ths or any other fractions.
4 1/10 bags = 41/10 bags
1 7/10 times = 17/10 times
and now we multiply fractions, as 17/10 times is similar to 2 times or 3 times something - we multiply by this factor.
41/10 × 17/10
as we learned in early elementary school : numerators (top part of the fraction) are multiplied with each other, and denominators (bottom part) are multiplied with each other. and then we simplify the result as much as possible.
41/10 × 17/10 = (41×17) / (10×10) = 697/100
no simplification is possible, sadly.
but that means he used almost 7 bags of hot dog buns.
exactly 6 full bags and 97/100 of the 7th bag.
so, either
697/100 bags
or
6 97/100 bags
or as alternative (not wanted here in this example but just FYI)
6.97 bags