Answer:
[tex]sin (70^{\circ})=cos (20^{\circ})[/tex]
Option C is correct.
Step-by-step explanation:
we have to choose the option for which the value is equals to sin(70°)
As in the first quadrant sine and cosine both are positive
[tex]\sin \theta = \cos (90-\theta)\\\\\sin (70^{\circ})= \cos (90-70)=\cos (20^{\circ})\\\\sin (70^{\circ})=cos (20^{\circ})[/tex]
hence, option C is correct.
The minimum value of a function is the smallest y-value of the function. A. True B. False
nine times five less than twice x
[tex]nine times fivelesstwicex[/tex]
A teacher asks her students to design a game board for a class project. The dimensions of the boards created by four students are shown below.
Angela
length: 20 cm
width: 21 cm
diagonal: 29 cm
Bradley
length: 9 in.
width: 9 in.
diagonal: 9 in.
Carlton
length: 25 cm
width: 30 cm
diagonal: 35 cm
Della
length: 10 in.
width: 12 in.
diagonal: 15 in.
Whose game board could be a rectangle?
Answer:
Angela's board is a rectangle.
Step-by-step explanation:
As we know rectangle follow two properties.
1). All angles of a rectangle are right angle.
2). Opposite sides of a rectangle are equal in measure.
Since all angles of a rectangle are 90°. Therefore, right angle triangle formed by length, width and diagonal will follow Pythagoras theorem.
For Angela
20² + 21² = 841 = 29²
Therefore Angela's board is a rectangle.
For Bradley
9² + 9² = 162 ≈ 9²
So Bradley's board is not a rectangle.
For Carlton
25² + 30² = 1525 ≠ 35²
Carlton's board is not a rectangle.
For Della
10² + 12² = 244 ≠ 15²
Della's board is not a rectangle.
Therefore, Angela's board is a rectangle.
What is the area of a figure whose vertices are (-2,1), (3,1), (2,-3), and (-3,-3)?
Instructions.find the volume and surface area of the rectangular prisms
I cant figure this out! please help.
solve for a.
3a+11.5
Determine b , given that A = 63°, C = 49°, and c = 3.
To find side b in the triangle, we use the fact that angles in a triangle sum up to 180° to find angle B, and then apply the Law of Sines to solve for b using angles B and C and side c.
To determine b in a triangle where angle A = 63°, angle C = 49°, and side c = 3, first, we need to find angle B using the fact that the sum of angles in a triangle is 180°. Therefore, B = 180° - A - C. Calculating this gives us B = 180° - 63° - 49° = 68°. Since angles A, B, and C are known, we can use the Law of Sines to find side b:
b/sin(B) = c/sin(C)
Rearranging this for b yields:
b = c * sin(B) / sin(C)
We substitute the known values to find b:
b = 3 * sin(68°) / sin(49°)
By solving this, we get the length of side b is 3.68
A right rectangular prism is shown. What shape best describes the cross section cut perpendicular to the base of a right rectangular prism? Parallelogram Trapezoid Rectangle Square
[tex] \frac{10.5}{1.79} [/tex]
[tex] \frac{16}{2.19} [/tex]
How would I find out the unit rate for these two equations?
the bill for a meal came to £65.40 plus 15% service charge what was the total bill?
To find the total bill including the service charge, multiply the original meal cost by 15% to calculate the service charge. Then, add this to the original meal cost to get the total of £75.21.
Explanation:The question involves Mathematics as it requires calculating the total bill including the service charge which is essentially calculating a percentage of the original amount. To determine the total amount to be paid, one must first calculate the 15% service charge on the £65.40 meal and add it to the original amount. The service charge is calculated by converting the percentage to a decimal and multiplying it by the meal cost: 0.15 × £65.40.
Let's do the calculation:
Find the service charge: 0.15 × £65.40 = £9.81Add the service charge to the original bill: £65.40 + £9.81 = £75.21The total bill after adding the 15% service charge to the £65.40 meal cost is £75.21.
The average number of mosquitoes in a stagnant pond is 70 per square meter with a standard deviation of 8 per square meter. if one square meter of the pond is chosen at random for a mosquito count, find the probability that the average of the count is more than 68 mosquitoes per square meter. assume that the variable is normally distributed.
The probability that the average mosquito count in a randomly chosen square meter of the pond is more than 68 mosquitoes is approximately 59.87%.
To find the probability that the average count of mosquitoes in a randomly chosen square meter of the pond is more than 68 mosquitoes per square meter, we can use the normal distribution properties.
Given:
Mean (">"): 70 mosquitoes per square meterStandard deviation (σ): 8 mosquitoes per square meterWe need to find P(X > 68). To do this, we convert the raw score to a Z-score using the formula:
Z = (X - μ) / σ
Substitute the given values:
Z = (68 - 70) / 8 = -2 / 8 = -0.25
Next, we need to find the probability corresponding to Z > -0.25 using the standard normal distribution table.
Looking up Z = -0.25, we find the cumulative probability (P(Z < -0.25)) is approximately 0.4013.
To find P(Z > -0.25):
P(Z > -0.25) = 1 - P(Z < -0.25) = 1 - 0.4013 = 0.5987
Therefore, the probability that the average mosquito count in a randomly chosen square meter is more than 68 mosquitoes per square meter is approximately 0.5987 or 59.87%.
what is the tenth rule for A(n)=-9+5(n-1)
At a pie-eating contest, Isla ate 1⁄4 of a pie before time was called. Alexa only finished 1⁄8 of a pie. How much more pie did Isla eat than Alexa?
Cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 after 3 years. What is the smallest amount, to the nearest pound, she can invest?
Simple steps please ?
Which equation could have been used to create this function table? 1 2,3 6,4 8,5 10, 10 20 A. y = 5x B. y = x + 1 C. y = x + 2 D. y = 2x
Try the first table value and see what you get from the various choices. For x = 1, the answer choices give you
... A: y = 5×1 = 5
... B: y = 1 + 1 = 2
... C: y = 1 + 2 = 3
... D: y = 2×1 = 2
Both B and D give the correct value (2), so we need to try another table entry. For x = 3 (the second table entry), the answer choices give you
... B: y = 3 + 1 = 4
... D: y = 2×3 = 6
Only selection D gives you the correct value (6). The appropriate choice is
... D. y = 2x
: Your experience indicates that offering a discount in your emails increases responses by 80%. Your last email, without a discount, got 23,000 responses. If you mail to the same size list and offer a discount, how many responses would you expect? a) 41,400 b) 44,000 c) 48,300 d) 52,400
The expected number of responses after offering a discount leads to an 80% increase from 23,000 is 41,400.
The student's question relates to predicting email response rates when a discount is offered. Since the history suggests an 80% increase in responses when a discount is included and the last email got 23,000 responses, we can expect:
Find the amount of increase in responses: 23,000 responses * 80% = 18,400 additional responses.Add the increase to the original number of responses: 23,000 responses + 18,400 added responses = 41,400 total expected responses.Thus, the answer is (a) 41,400 responses expected with a discount offer.
T-shirts at a clothing store cost $19 each Rory bought several T-shirts at this price and paid $57 how many t-shirts did Rory buy
Tory plans to enter the path at mile marker 1 and hike for 4 miles. Tory is a beginner hiker, so he wants to choose the path that is less steep on average.
Which path should he choose? Why?
PLEASE HELLPPPP!!!!!!!!!!!!
Figure BMHF is rotated how many degrees clockwise?
the median of the values in a data set is y. if 48 were subtracted from each of the values in the data set what would be the median of the resulting data
Answer: Y-48
If the median of the values in the data set is Y, it means that Y is the value in the middle of the data set. If 48 will be deducted from each of all values in the data set including Y, then the median of the resulting value will be Y-48.
If the perimeter of a rectangle is 52 cm and the area is 165 square cm, then what are the dimensions of the rectangle?
Answer:
11 cm by 15 cm
Step-by-step explanation:
The perimeter is double the sum of length and width, so that sum is 26 cm. The area is the product of length and width, so you want to find two numbers whose product is 165 and whose sum is 26.
165 = 1·165 = 3·55 = 5·33 = 11·15
The numbers in the last factor pair total 26. These are the dimensions.
The dimensions are 11 cm by 15 cm.
What is the domain of the function y= square root x?
Answer:
[0, ∞) or 0 ≤ x
Step-by-step explanation:
You want to know the domain of the function y = √x.
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. The square root function is defined for all non-negative real numbers. So, ...
The domain of
y = √x
is all real numbers greater than or equal to zero.
0 ≤ x . . . . domain of y=√x
In interval notation, this is ...
[0, ∞) . . . . domain of y=√x
__
Additional comment
The inequality for the domain of y=√x can also be written as x ≥ 0.
It is sometimes useful to write the inequality with a left-pointing inequality symbol so the limit and the variable map directly to a region of the number line. Here, the limit (0) is at the left end of the ray on the number line that identifies the domain of x.
The "practical" domain of a function is the set of values the function may be expected to utilize in the real world. A function may be defined for all values of mass, for example, but is of no practical use for negative mass or values of mass greater than that of the known universe.
Final answer:
The domain of the function y = √x consists of all real numbers greater than or equal to 0. The function is non-differentiable only at x = 0. The restriction ensures that the square root is of a non-negative number, conforming to real-valued outputs.
Explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined. Considering the function y = √x, the domain is all real numbers greater than or equal to 0 because we cannot take the square root of a negative number in the real number system. This ensures that the values under the square root are non-negative, allowing the function to produce real number outputs. When we consider functions like l(x) = x² √√x, we must also consider that while x² is defined for all real numbers, the part √√x restricts the domain since x must be greater than or equal to 0 for the function to be real-valued. Thus, the domain of l(x) is also limited to x values greater than or equal to 0.
When seeking nondifferentiable points within the domain, we look for values of x where the derivative of the function does not exist. For the function y = √x, all points in the domain are differentiable except at x = 0, where the function has a cusp and is, therefore, not differentiable.
To summarize, the domain of y = √x is all x ≥ 0, and with the function l(x), we are careful to include only those x-values where the square root and the entire expression are defined, which also turns out to be x ≥ 0.
simplify 3 square root of 2 minus square root of 2
Explain how you can tell when a formula represents a length an area or a volume
Area and volume are both used to determine the amount of space.
While area is used for two-dimensional shapes, volume is used for three-dimensional shapes.
The difference between the given parameters are:
Length is often represented as the difference between points.Area is represented as the product of two dimensions or the square of a dimensionVolume is represented as the product of three dimensions or the cube of a dimensionFor instance:
[tex]\mathbf{Length = b -a}[/tex]
[tex]\mathbf{Area = ab}[/tex]
[tex]\mathbf{Volume= abc}[/tex]
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If a quantity you calculated has units of (kg*m^2)/(s^2*c), what is that quantity?
Final answer:
The quantity with units of (kg*m²)/(s²*c) is closely related to the energy concept in physics, specifically within the framework of Einstein's mass-energy equivalence formula, E = mc², albeit with an added factor of the speed of light in the denominator.
Explanation:
The quantity with units of (kg*m^2)/(s^2*c) is related to the concept of mass-energy equivalence, as seen in Albert Einstein's famous equation, E = mc².
In this equation, E represents energy in joules, m represents mass in kilograms, and c represents the speed of light in meters per second.
The units of c² are m²/s², making the units of energy (when mass is given in kilograms) equivalent to kg*m²/s², or joules.
However, the specific units you mentioned, (kg*m²)/(s²*c), seem to incorporate an additional factor of the speed of light in the denominator, suggesting a possible deviation or specific application within the broader context of relativistic physics or energy conversions where the factor of c is explicitly considered.
tanθ=sinθ/cosθ
True or False
Leslie is a biologist. She is going to randomly select one animal from her lab to study. There are 5 salamanders, 3 crayfish, and 12 minnows in her lab. What is \text{P(salamander}
The sample space contains three types of animals; 5 salamanders, 3 crayfish, and 12 minnows.
So population of sample space would be, n(S) = Salamanders + Crayfish + Minnows.
n(S) = 5 + 3 + 12 = 20.
She wants to randomly select an animal and check if it is Salamander or not.
population of favourable outcomes would be, n(salamander) = 5.
Now the probability for selecting a salamander would be :-
[tex]P(salamander) = \frac{n(salamander)}{n(S)} \\\\ P(salamander) = \frac{5}{20} \\\\ P(salamander) = \frac{1}{4} \;or\; 0.25 \;or\; 25\%[/tex]
A work cell is scheduled to build 120 digital light processor (dlp) assemblies each week. these assemblies are later installed into home theater projection systems. the work cell has 7.5 hours of productive work each day, six days per week. what is takt time for this cell? express your answer in minutes rounded to one decimal place.
41 packages are randomly selected from packages received by a parcel service. the sample has a mean weight of 20.6 pounds and a standard deviation of 3.2 pounds. what is the best pint estimate for a confidence interval estimating the true mean weight, μ, of all packages received by the parcel service? answer: _____pounds
The best point estimate for the true mean weight of all packages received by a parcel service, given a sample mean of 20.6 pounds and a standard deviation of 3.2 pounds, is 20.6 pounds.
Explanation:In this problem, we are given that a sample of 41 packages were randomly selected. This sample provided a mean weight of 20.6 pounds and a standard deviation of 3.2 pounds. It is asked what the best point estimate for a confidence interval estimating the true mean weight of all packages is.
The best estimate of the true mean weight (µ) of all packages would be the mean of the sample that was taken, assuming that the sample was randomly selected and is representative of the entire population. This is due to the fact that in statistics, the sample mean is the best point estimate of the population mean.
Therefore, the best point estimate for the true mean weight of all the packages received by the parcel service is 20.6 pounds.
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Describe how you could draw a diagram for a problem about finding the total length for two strings, 15 inches long and 7 inches long