Answers
Answer:
[tex]a =\frac{\sqrt 2}{2}[/tex] m
[tex]b=\frac{\sqrt 2}{2}[/tex] m
Step-by-step explanation:
Given
The attached triangle
Required
Find a and b
To do this, we make use of the following trigonometry ratio
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
So, we have:
[tex]\sin(45) = \frac{a}{c}[/tex]
[tex]\sin(45) = \frac{b}{c}[/tex]
Where
[tex]c = 1[/tex]
So, we have:
[tex]\sin(45) = \frac{a}{1}[/tex]
[tex]\sin(45) = a[/tex]
Rewrite as:
[tex]a =\sin(45)[/tex]
In radical form:
[tex]\sin(45) =\frac{\sqrt 2}{2}[/tex]
So:
[tex]a =\frac{\sqrt 2}{2}[/tex]
Similarly:
[tex]\sin(45) = \frac{b}{c}[/tex]
[tex]\sin(45) = \frac{b}{1}[/tex]
[tex]\sin(45) = b[/tex]
Rewrite as:
[tex]b = \sin(45)[/tex]
In radical form:
[tex]\sin(45) =\frac{\sqrt 2}{2}[/tex]
So:
[tex]b=\frac{\sqrt 2}{2}[/tex]
Related Questions
The 4th grade class experienced a 15% decrease in enrollment. Last year, the 4th grade class had 280 students. How many students are enrolled in the 4th grade class this year?
Answers
Answer: 238
Step-by-step explanation: 15% of 280 is 42 so subtract 42 from the number and it equals 238
A triangle has an area of 144 square feet. The height is 24 feet. What is the length of the base(in feet)?
Answers
Answer:
Base = 12
Step-by-step explanation:
Because
24 x 12 = 288 divide by 2 and you get are area 144
So we have: h.b/2=Area
24.b/2=144
24.b=144.2
24.b=288
b=288/24= 12
So the base is 12
Here is a 95% confidence interval estimate of the proportion of adults who say that the law goes easy on celebrities: 0.692 < p < 0.748 (based on data from a Rasmussen Reports survey). a.What is the best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities
Answers
Answer:
The best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities is 0.72.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used(best point estimate) is the mid point between these two bounds, that is, the mean of the two bounds.
In this question:
The two bounds are 0.692 and 0.748.
a.What is the best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities.
The mean of the bounds, so:
(0.692+0.748)/2 = 0.72
The best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities is 0.72.
A dealer bought a refrigerator for $ 11515. After allowing a discount of 16% on its marked price, he gains 20%. Find the marked price of the refrigerator.
Answers
Given:
Cost price of refrigerator = $11515
Discount rate 16% on its marked price.
Profit = 20%
To find:
The marked price of the refrigerator.
Solution:
The cost price (C.P.) is $11515 and the profit percent is 20%. So, the selling price is:
[tex]S.P.=C.P.+20\%\text{ of }C.P.[/tex]
[tex]S.P.=11515+\dfrac{20}{100}(11515)[/tex]
[tex]S.P.=11515+2303[/tex]
[tex]S.P.=13818[/tex]
Let x be the marked price of the refrigerator. Then,
[tex]S.P.=x-16\%\text{ of }x[/tex]
[tex]13818=x-\dfrac{16}{100}x[/tex]
[tex]13818=x-0.16x[/tex]
[tex]13818=0.84x[/tex]
Divide both sides by 0.84.
[tex]\dfrac{13818}{0.84}=x[/tex]
[tex]16450=x[/tex]
Therefore, the marked price of the refrigerator is $16450.
how do you do this I really need some help!please
Answers
Answer:
It is correct for 5. Incorrect for 6. Lastly, correct for 7.
Answer:
yes
no
yes
Step-by-step explanation:
you plug in the 3 into the x, because x=3 so therefore 3+5>7 which becomes 8>7. Is 8 more than 7? yes! so its true. For the next, 7>12, thats not true. And for the last one, 10-7<5, so 3<5, which is true.
!NO LINKS, NO FILES!
please :)
Answers
Answer:
B...?
Step-by-step explanation:
Either B or D so use your skills to find out ;)
A large fish tank measures 24 x 12 x 16 inches. If the tank is filled to the top, how much water will fill the tank?
Answers
Answer:
4608
Step-by-step explanation:
24 x 12 x 16 = 4608
Deacon wants to order DVDs. Each DVD costs $12.95, and he must pay a shipping and handling fee of $4.95 for the entire order. Deacon must spend no more than the $75 gift card he has.
Which inequality matches the situation?
Answers
Answer:
12.95a + 4.95 ≤ 75
Step-by-step explanation:
Given:
Cost of each DVD = $12.95
Total shipping fee = $4.95
Total amount as gift card = $75
Find;
Inequality
Computation:
Assume;
Number of DVD he purchase = a
So,
Total amount as gift card ≥ (Cost of each DVD)(Number of DVD he purchase ) + Total shipping fee
75 ≥ (12.95)(a) + 4.95
12.95a + 4.95 ≤ 75
1) 14, 16, 18, 20, 22, ...
A) 29, 32, 35 B) 24, 26, 28
C) 34, 38, 42 D) 28, 31, 34
Answers
Answer:
What should we do the question pls
Find the indicated side of the
right triangle.
60°
х
7
30°
x = [?]
Enter
Answers
Here's the solution,
By using Trigonometry :
=》
[tex] \sin(30) = \dfrac{7}{x} [/tex]
=》
[tex] \dfrac{1}{2} = \dfrac{7}{x} [/tex]
=》
[tex]x = 14[/tex]
hence, the value of x = 14 units
Answer:
14
Step-by-step explanation:
ratio of 5 cm to 25 cm.
C/
2.
Answers
Answer:
1:5
Step-by-step explanation:
5/5 and 25/5
so 1:5
Info Details Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 22 of the 63 boxes on the shelf have the secret decoder ring. The other 41 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that both of them have the secret decoder ring
Answers
Answer:
0.1183 = 11.83% probability that both of them have the secret decoder ring.
Step-by-step explanation:
The boxes are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
63 boxes means that [tex]N = 63[/tex]
22 have the secret decoder ring, which means that [tex]k = 22[/tex]
Two are selected, which means that [tex]n = 2[/tex]
What is the probability that both of them have the secret decoder ring?
This is P(X = 2). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,63,2,22) = \frac{C_{22,2}*C_{41,0}}{C_{63,2}} = 0.1183[/tex]
0.1183 = 11.83% probability that both of them have the secret decoder ring.
What is the measure of the unknown acute angle in this right triangle?
Answers
Answer:
The answer is 54
Step-by-step explanation:
36+90=126
180-126= 54
Answer:
54 degrees
Step-by-step explanation:
what is the volume of the triangular prism with b=7in, h=5in and H=12.7in?
Answers
Answer:
444.5 in³
Step-by-step explanation:
This is a quite interesting question.
Here are some formulas to help you,
Volume= L*b*h
Height = Volume/ L*b
Length= Volume/h*b
Breadth= Volume/l*h
For this question, we will consider the first formula.
Volume= Length* Breadth* Height
Volume= 5 in * 7 in * 12.7
Volume= 444.5 in³
PLease give me answer ASAP
Answers
Answer:
Step-by-step explanation:
Answer:
the answer is get noob..........
PLEASE HELP————————-
Answers
What is the probability of drawing a blue gumdrop from a candy jar if it contains 6 green, 7 yellow, 1 white and 4 blue gumdrops?
Answers
Explanation:
4 : 18
There are 4 blue marbles out of a total of 18 marble. 4 and 18 are both divisible my 2 so you reduce it to get 2:9.
I will give you Brainliest and 500 points if you do this please
Answers
Answer:
1. C
2. D
Step-by-step explanation:
1.
Pattern A is adding by 2's (1 -> 3, 4 -> 6, 7 -> 9 and so on).
Pattern B is multiplying by 2's (2 -> 4, 3 -> 6, 4 -> 8 and so on).
2.
If 0.25 gallons of paint = 24 ft^2, then 1 gallon will equal?
Set up an equation:
Variable x = area of ft^2 for 1 gallon of paint
0.25/24 = 1/x
Cross multiply
0.25 × x = 24 × 1
0.25x = 24
To make calculations easier, you can convert the decimal into a fraction: 0.25 = 1/4
1/4x = 24
Multiply both sides by 4
1x = 96
x = 96 ft^2
Check your work:
0.25/24 = 1/96
0.25 × 96 = 24 × 1
24 = 24
Correct
A newspaper conducted a statewide survey concerning a proposal to raise taxes to prevent budget cuts to education. The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 580 would vote to raise taxes. Let p represent the proportion of registered voters in the state that would vote to raise taxes.Reference: Ref 20-4How large a sample n would you need to estimate p with margin of error 0.01 with 90% confidence
Answers
Answer:
A sample of 6758 would be needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 580 would vote to raise taxes.
This means that [tex]\pi = \frac{580}{1200} = 0.4833[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
How large a sample n would you need to estimate p with margin of error 0.01 with 90% confidence?
This is n for which M = 0.01. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.01 = 1.645\sqrt{\frac{0.4833*0.5167}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.645\sqrt{0.4833*0.5167}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.4833*0.5167}}{0.01}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645\sqrt{0.4833*0.5167}}{0.01})^2[/tex]
[tex]n = 6757.5[/tex]
Rounding up:
A sample of 6758 would be needed.
A popcorn cup is in the shape of a cone. The slant height of the cone is 9 inches, and the diameter is 6.2 inches. What is the volume of the cone? Use pi equals 3.14.
Answers
Answer:
V = 262.61 m³
Step-by-step explanation:
Given: Slant height of the cone is 9 inches, the diameter is 6.2 inches.
Formula: The formula for the volume of a cone is V = 1/3hπr².
Solve: V = 262.610935 m³
graph the line with y-intercept 5 and slope 2
Answers
Answer: y = mx + b
Step-by-step explanation:
Answer:
y=mx+b
Step-by-step explanation:
Hope it helps u
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I need help with this if you’re right I will mark you as brainlest
Answers
Answer:
try 1.8 or .18
Step-by-step explanation:
Which of the following terms correctly describe the object below?
Check all that apply.
A. Polygon
B. Pyramid
C. Triangle
D. Prism
E. Polyhedron
F. Square
Answers
Answer:
pyramid, solid, polyhedron
Step-by-step explanation:
The given figure is a pyramid.
What is a pyramid?A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point. A pyramid is formed by connecting the bases to a vertex. Each edge of the base is connected to the vertex, and forms the triangular face, called the lateral face.
The given figure is a square pyramid, since it has a square base where all the edges are joined at a common vertex by four triangular faces. A square pyramid characterized by a square base is a three-dimensional shape having five faces, thus called a pentahedron. The most famous example of such a square pyramid is the Great Pyramid of Giza.
Learn more about pyramid here
https://brainly.com/question/13057463
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What is the period of y=4cos5x
Answers
you take 2pi and divide it by bits stolen from the equation its explained more in the screennshot
53
Given that the measure of angle Xis 132º, and the measure of angle Yis 55°, find the
measure of Angle z
Answers
Andrew has 2 cats and 9 dogs. He writes the ratio 2:9. What does this ratio mean? *
Answers
Answer:
it means that for every two cats there are nine dogs, so if they were four cats there'll be 18 dogs and so on
Answer:
Two cats per nine dogs
Step-by-step explanation:
The ratio is two cats to nine dogs, meaning that for every two cats, there are nine dogs, and vice versa. This applies to any ratio. Hope this helps! Feel free to ask any questions!
Find the angular size of a circular object with a 1-inch diameter viewed from a distance of 4 yards.
The angular size of the object is Iº.
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
Answers
Answer:
0.40°Step-by-step explanation:
4 yards = 4*36 in = 144 inAngle is x
tan(x/2) = 1/2 * 1/144x/2 = arctan (1/288)x /2 = 0.1989428794619145°x = 2*0.1989428794619145°x = 0.39788575892° x = 0.40° (rounded)2. GIVING BRAINLIEST FOR CORRECT ANSWER WITH EXPLANATION
Answers
Answer:
its 5
Step-by-step explanation:
F(6) = 2(6)^2 + 5 sqrt(6-2)
Answers
Answe well this look complicated gimme some time
Step-by-step ex
There are 46 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 4 min. (Round your answers to four decimal places.) A button hyperlink to the SALT program that reads: Use SALT. (a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins
Answers
Answer:
0.7704 = 77.04% probability that he is through grading before the 11:00 P.M. TV news begins
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Distribution of n values from a normal distribution:
If we take n values from a normally distributed variable, the mean is [tex]\mu*n[/tex], and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
There are 46 students in an elementary statistics class. For each student, the mean is of 5 min and a standard deviation of 4 min.
This means that
[tex]\mu = 46*5 = 230[/tex]
[tex]s = 4\sqrt{46} = 27.13[/tex]
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
This is the probability that he finishes grading in 4 hours and 10 minutes, that is, 4*60 + 10 = 250 minutes, which is the pvalue of Z when X = 250.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In this distribution
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{250 - 230}{27.13}[/tex]
[tex]Z = 0.74[/tex]
[tex]Z = 0.74[/tex] has a pvalue of 0.7704
0.7704 = 77.04% probability that he is through grading before the 11:00 P.M. TV news begins