Answer:
56
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
75 = 1/2 (94+d)
Multiply by 2
75*2 = 94+d
150 = 94+d
Subtract 94 from each side
150-94 = d
56=d
A fruit company delivers its fruit in 2 types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 79 kilograms. A delivery of 12 large boxes and 2 small boxes has a total weight of 199 kilograms. How much does each type of box weight?
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Answer:
large: 15.5 kgsmall 6.5 kgStep-by-step explanation:
Let x and y represent the weights of the large and small boxes, respectively. Then the two delivery weights give rise to the equations ...
3x +5y -79 = 0
12x +2y -199 = 0
Using the "cross multiplication method" of solving these equations, we find ...
d1 = (3)(2) -(12)(5) = 6 -60 = -54
d2 = 5(-199) -(2)(-79) = -995 +158 = -837
d3 = -79(12) -(-199)(3) = -948 +597 = -351
1/d1 = x/d2 = y/d3
x = d2/d1 = -837/-54 = 15.5
y = d3/d1 = -351/-54 = 6.5
The large boxes weigh 15.5 kg; the small boxes weigh 6.5 kg.
_____
Additional comment
My preferred quick and easy way to solve equations like this is using a graphing calculator. In addition to that, an algebraic method is shown.
The "cross-multiplication method" shown here is what I consider to be a simplified version of what you would find in videos. It is a variation of Cramer's rule and the Vedic maths methods of solving pairs of linear equations. I find it useful when "elimination" or "substitution" methods would result in annoying numbers. In such cases, it uses fewer arithmetic operations than would be required by other methods.
Short description: writing the coefficients of the general form equations in 4 columns, where the last column is the same as the first, a "cross multiplication" is computed for each of the three pairs of columns. Those computations are of the form ...
[tex]\text{column pair: }\begin{array}{cc}a&b\\c&d\end{array}\ \Rightarrow\ d_n=ad-cb[/tex]
The relationship between the differences d₁, d₂, and d₃ and the variable values is shown above.
what is the measure of m?
The required value of m for the given triangle is given as m = 12.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
Applying Pythagoras' theorem,
n² = m² - 6² - - - - (1)
m ² + base² = 24²
base² = 24² - m² - - - - (2)
n² + 18² = base²
From equation 1 and 2
m² - 6² + 18² = 24² - m²
2m² = 24² + 6² - 18²
m = 12
Thus, the required value of m for the given triangle is given as m = 12.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ2
What value of x makes the equation 3x+7=22 true?
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
Given [tex]3x+7=22[/tex], our goal is to isolate [tex]x[/tex] such that will have an equation that tell us [tex]x[/tex] is equal to something.
Start by subtracting 7 from both sides:
[tex]3x+7-7=22-7,\\3x=15[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3}=\frac{15}{3},\\x=\frac{15}{3}=\boxed{5}[/tex]
Therefore, the value of [tex]x=5[/tex] makes the equation [tex]3x+7=22[/tex] true.
Answer:
x = 5
Step-by-step explanation:
Subtract 7 from both sides: 3x + 7- 7 = 22 - 7
Simplify: 3x = 15
Divide both sides by 3
Simplify: x = 5
Hope this helps:)
the legs of a right triangle have the following measurements: 5 and 10 inches. What is the length of the hypotenuse??
Write your answer in SIMPLIFIED SQUARE ROOT FORM
Answer:
[tex]5\sqrt{5}[/tex]
Step-by-step explanation:
1. [tex]5^2 + 10^2 = c^2[/tex]
2.[tex]125 = c^2[/tex]
3. [tex]c=5\sqrt{5}[/tex]
What are the equations of the asymptotes for the functiony=tan2pix where 0
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Answer:
(b) x = 0.25, 0.75, 1.25, 1.75
Step-by-step explanation:
The asymptotes of tan(α) are found at ...
α = π/2 +nπ
We want to find x such that ...
2πx = α = π/2 +nπ
Dividing by 2π gives ...
x = 1/4 +n/2 . . . . . . . for integers n
In the desired range, the values of x are ...
x = 0.25, 0.75, 1.25, 1.75
Can someone help me out please
The following data on price () and the overall score for stereo headphones that were tested by Consumer Reports were as follows. The estimated regression equation for these data is
(y-hat) = 27.922+0.302x
Brand Price Score
Bose 180 76
Scullcandy 160 76
Koss 95 69
Phillips/O'Neill 70 58
Denon 80 50
JVC 35 26
Required:
Does the t test indicate a significant relationship between price and the overall score?
Answer:
Relationship exists between price and overall score
Step-by-step explanation:
Given the data:
Brand Price Score
Bose 180 76
Scullcandy 160 76
Koss 95 69
Phillips/O'Neill 70 58
Denon 80 50
JVC 35 26
Using the correlation Coefficient calculator ; the correlation Coefficient, R = 0.875
H0 : no relationship exists
H1 : relationship exists
Using the R Coefficient ;
The test statistic :
T = r / √(1 - r²) / (n - 2)
n = 6
The test statistic :
T = 0.875 / √(1 - 0.875²) / (4)
T =0.875 / 0.05859375
T = 0.9333
The Pvalue from test statistic :
df = n - 2 ; 6 - 2 = 4
Pvalue(0.933, 4) = 0.02246
At α = 0.05
Pvalue < α ; We reject H0 ; and conclude that relationship exists between price and overall score
66. If the length of one side of a triangle 6 and the length of another side is 2, which of the following cannot be the length of the third side of the triangle?
A) 8
B) 7
C)
D) 5
Answer:
A)
Step-by-step explanation:
what is C ? 6 ?
if that is the case, then my answer is A) 8
why ? because then the other 2 sides together are just as long as this third side, and we would have just a flat line with the length of 8.
every side in a triangle must be shorter than the other two sides together.
but - fully formally such a flat line could be considered a special triangle with 2 angles of 0 degrees and one angle of 180 degrees.
that is why I am asking about the missing C answer. it could be a trick question. but if C is truly 6, then yes, A is the right answer. if C is larger than 8, then C is the right answer.
write your answer in simplest radical form
Answer:
n = 8√2
Step-by-step explanation:
It's a 30-60-90 triangle, so n = 2×4√6/√3 = 8√2
Needs 20 characters even though the picture says it all.
Daphne has a rope that is 60 meters long. She wants to use it to mark the boundary of a circle whose radius is an integer. What's the largest possible radius for her circle, in meters?
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Answer:
9 m
Step-by-step explanation:
The relationship between radius and circumference is ...
C = 2πr
Daphne wants r an integer such that ...
60 m ≥ 2πr
r ≤ (60 m)/(2π)
r ≤ (30/π) m ≈ 9.549 m
The largest integer radius Daphne can use is 9 meters.
What is the x- intercept y =2x^2-8x+6?
Answer:
see your answer in the image
with full detail
mark me brainlist
Step-by-step explanation:
Answer:
(3,0) , (1.0)
Step-by-step explanation:
Eric wrote the number 57,378. How many
times greater is the value of the 7 in the thousands
place than in the tens place?
When taking a measurement with a pH meter, keep the instrument in the Choose... until it is needed. Rinse the pH meter with Choose... and gently pat dry. Place the meter in the sample solution, and record the measurement when the
Answer:
Storage solution; deionized water; stabilizes
Step-by-step explanation:
A pH scale measures the concentration of hydrogen ions in acidic and alkaline solutions.
In chemistry, pH literally means the power of hydrogen ions and it is a measure of the molar concentration of hydrogen ions in a particular solution; thus, specifying the acidity, neutrality or basicity of any chemical solution.
Mathematically, the pH of a solution is given by the formula;
[tex] pH = -log_{10}(H^{+}) [/tex]
On a pH scale, a solution with a pH of 7 is neutral, a solution with a pH below 7 is acidic and it's basic (alkaline) when it's pH is above 7.
A pH meter can be defined as a scientific instrument or device designed and developed for the measurement of the hydrogen-ion concentration in water-based solutions, in order to determine their level of acidity or alkanility.
As a general rule, when using a pH meter to take a measurement, you should keep it in a storage solution until it is needed. Also, a deionized water should be used to rinse the pH meter and gently pat dry.
Furthermore, the pH meter should be placed in a given sample solution and a reading of the measurement taken when the pH of the solution stabilizes
When taking a measurement with a pH meter, keep the instrument in the storage solution until it is needed. Rinse the pH meter with distilled water and gently pat dry.
The pH meter has been the instrument used for the measurement of the hydrogen ion concentration in a sample. The instrument has consisted of a probe that has been placed in the storage medium when it is not in use.
The working procedure of the pH meter has required the washing of pH meter with the distilled water and properly removing the excess water from the probe by pat dry.
The probe has been immersed in the sample and the pH has been recorded. After the experiment, the instrument has been again washed with the distilled water and get stored in the storage solution.
For more information about pH meter, refer to the link:
https://brainly.com/question/14777354
I need Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Answer:
150.72 cm³314 cm³160 cm³48 cm³Step-by-step explanation:
Put the given numbers in the relevant formula and do the arithmetic.
right cylinder
V = πr²h = 3.14(4 cm)²(3 cm) = 3.14×48 cm³ = 150.72 cm³
cone
V = 1/3πr²h = 1/3(3.14)(5 cm)²(12 cm) = 3.14×100 cm³ = 314 cm³
pyramid of unknown shape
V = 1/3Bh = 1/3(16 cm²)(30 cm) = 160 cm³
square pyramid
V = 1/3s²h = 1/3(3 cm)²(16 cm) = 48 cm³
What are the solutions to the quadratic equation x^2-16=0
Answer:
x = ±4
Step-by-step explanation:
Hi there!
[tex]x^2-16=0[/tex]
Move 16 to the other side
[tex]x^2=16[/tex]
Take the square root of both sides
[tex]\sqrt{x^2}=\sqrt{16}\\x=\pm4[/tex]
I hope this helps!
Module 8: Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Describe how to eliminate the parameter to change from parametric to rectangular form. How does this ability help us with graphing parametric equations?
Answer:
rectangular equation, or an equation in rectangular form is an equation composed of variables like xx and yy which can be graphed on a regular Cartesian plane. For example y=4x+3y=4x+3 is a rectangular equation.
A curve in the plane is said to be parameterized if the set of coordinates on the curve, (x,y)(x,y) , are represented as functions of a variable tt .
x=f(t)y=g(t)x=f(t)y=g(t)
These equations may or may not be graphed on Cartesian plane.
Step-by-step explanation:
I hope this helps
In 1995 the U.S. federal government debt totaled 5 trillion dollars. In 2008 the total debt reached 10 trillion dollars. Which of the following statements about the doubling time of the U.S. federal debt is true based on this information?
Where are the statements?
Write an expression representing the unknown quantity.
There are 5,682,953 fewer men than women on a particular social media site. If x represents the number of women using that site, write an expression for the number of men using that site.
The expression for the number of men is
.
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Answer:
x - 5,682,953
Step-by-step explanation:
If x is the number of women, and the number of men is 5,682,953 less, then the number of men is x -5,682,953
Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
A: Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
B: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
C: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Answer:
D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Jarvis invested some money at 6% interest. Jarvis also invested $58 more than 3 times that amount at 9%. How much is invested at each rate if Jarvis receives $1097.19 in interest after one year? (Round to two decimal places if necessary.)
Use the variables x and y to set up a system of equations to solve the given problem.
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Answer:
$3309 at 6%$9985 at 9%Step-by-step explanation:
Let x and y represent amounts invested at 6% and 9%, respectively.
y = 3x +58 . . . . . . . the amount invested at 9%
0.06x +0.09y = 1097.19 . . . . . . total interest earned
__
Substituting for y, we have ...
0.06x +0.09(3x +58) = 1097.19
0.33x + 5.22 = 1097.19 . . . . . . . . . simplify
0.33x = 1091.97 . . . . . . . . . . . . subtract 5.22
x = 3309 . . . . . . . . . . . . . . . . divide by 0.33
y = 3(3309) +58 = 9985
$3309 is invested at 6%; $9985 is invested at 9%.
Find the tangent line equations for the given functions at the given point(s): f(x) = tan x + 9 sin x at (π, 0)
Answer:
[tex]{ \bf{f(x) = \tan x + 9 \sin x }}[/tex]
For gradient, differentiate f(x):
[tex]{ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}[/tex]
Substitute for x as π:
[tex]{ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}[/tex]
Gradient of tangent = -8
[tex]{ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi[/tex]
Equation of tangent:
[tex]{ \boxed{ \bf{y = - 8x + 8\pi}}}[/tex]
Solve the following equation for
a
a. Be sure to take into account whether a letter is capitalized or not.
Answer:
6/5 n = a
Step-by-step explanation:
n = 5/6a
Multiply each side by 6/5
6/5 n = 6/5 * 5/6a
6/5 n = a
Rachel and Hugo sorted 236 crayons into boxes for a local arts project. Each box had 10 crayons. How many crayons were left over?
Help please lol
Answer:
6
Step-by-step explanation:
236/10 = 23 remainder 6, so 6 crayons is the answer
The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.09 kWh. A previous study found that for an average family the variance is 5.76 kWh and the mean is 16.6 kWh per day. If they are using a 98% level of confidence, how large of a sample is required to estimate the mean usage of electricity
Answer:
A sample of 3851 is required.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a pvalue of , so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Variance is 5.76 kWh
This means that [tex]\sigma = \sqrt{5.76} = 2.4[/tex]
They would like the estimate to have a maximum error of 0.09 kWh. How large of a sample is required to estimate the mean usage of electricity?
This is n for which M = 0.09. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.09 = 2.327\frac{2.4}{\sqrt{n}}[/tex]
[tex]0.09\sqrt{n} = 2.327*2.4[/tex]
[tex]\sqrt{n} = \frac{2.327*2.4}{0.09}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*2.4}{0.09})^2[/tex]
[tex]n = 3850.6[/tex]
Rounding up:
A sample of 3851 is required.
Which answer choice correctly identifies the extraneous information in the problem?
Anna babysat 2 children on Saturday night. She charges $8 an hour to babysit. She wants to save the money she earns babysitting to buy a stereo system that cost $225. If Nina babysat for 5 hours, how much money did she earn?
Answer: $40 / $80
Step-by-step explanation: 40$ if it's $8 for BOTH per hour, or if it's $8 for ONE per hour it's $80
Student Engineers Council at an Indiana college has one student representative from each of the five engineering majors (civil, electrical, industrial, materials, and mechanical). Compute how many ways a president, a vice president, and a secretary can be selected.
Answer:
A president, a vice president, and a secretary can be selected in 60 ways.
Step-by-step explanation:
The order in which the people are chosen is important(first president, second vice president and third secretary), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
3 students from a set of 5, so:
[tex]P_{(5,3)} = \frac{5!}{2!} = 5*4*3 = 60[/tex]
A president, a vice president, and a secretary can be selected in 60 ways.
I need help ASAP is anyone available
Answer:
C
Step-by-step explanation:
The graph has asymptotes at x = 2 and x = -1 corresponding to the denominator of option C.
Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3
What is lim f(x)?
Answer:
[tex]\displaystyle 51[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringFunctionsFunction NotationAlgebra II
Piecewise functionsCalculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
Limit Property [Multiplied Constant]: [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]
Step 2: Solve
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 2^+} 6(2x - 1)^2 - 3[/tex]Factor: [tex]\displaystyle \lim_{x \to 2^+} 3[2(2x - 1)^2 - 1][/tex]Rewrite [Limit Property - Multiplied Constant]: [tex]\displaystyle 3\lim_{x \to 2^+} 2(2x - 1)^2 - 1[/tex]Evaluate [Limit Property - Variable Direct Substitution]: [tex]\displaystyle 3[2(2 \cdot 2 - 1)^2 - 1][/tex]Simplify: [tex]\displaystyle 51[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
PLEASE HELP please I need this done now
The total cost of a truck rental, y, for x days, can be modeled by y = 35x + 25.
What is the rate of change for this function?
Answers
A- 35$
B-25$
C-60$
D-10$
Answer:
35
Step-by-step explanation:
y = 35x+23 is in the form
y = mx+b where m is the slope and b is the y intercept
The slope can also be called the rate of change
35 is the slope
