Answers
Answer:
A) 41 degrees
Step-by-step explanation:
A) SohCahToa
20 = hyp.
15 = adj.
therefore, use Cos (Cah).
cos x = 15/20
x= cos^-1 (15/20)
x= 41 degrees
The required values are shown below.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.
Since, All the triangle are right angle triangle.
Use right angle properties,
(a)
To find the value of θ,
Use cos θ = base/hypotenuse = 15 / 20 = 3/4
cos θ = 3/4
θ = cos⁻¹ (3/4)
θ = 41.41
The value of θ is 41.41°.
(b)
Use sin θ = 3/10 =
θ = 17.45
The value of θ is 17.45.
(c)
Use Pythagorean theorem,
x² + x² = 5²
2x² = 25
x² = 25/2
x = 5/√2
(d)
sin30 = x / 8
1/2 = x/8
x = 4
cos 30 = y / 8
√3 / 2 = y/8
y = 4√3
The values of x and y are 4 and 4√3 respectively.
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Related Questions
Which figure has one line of symmetry but no rotational symmetry?
Answers
Answer:
c because u can split it only once vertically but it’s not a rotationally symmetrical shape
Step-by-step explanation:
Suppose Tommy walks from his home at (0, 0) to the mall at (0, 7), and then walks to a movie theater at (9, 7). After leaving the theater Tommy walks to the store at (9, 0) before returning home. If each grid square represents one block, how many blocks does he walk?
Answers
Answer:
32 blocks
Step-by-step explanation:
distance between home (0,0) and mall (0,7) = 7
distance between mall (0,7) and movies (9,7) = 9
distance between movies (9,7) and store (9,0) = 7
distance between store (9,0) and home (0,0) = 9
7 + 9 + 7 + 9 = 32 blocks
what number should be placed in the box to help complete the division calculation
Answers
Answer:
15
Step-by-step explanation:
12 X 15 is 180, which is closest to 187, we have to add a 5 in the space next to 71 and 180 under 187
If two lines intersect , then they intersect in exactly one
Answers
Answer:
point?
Step-by-step explanation:
is this a question or a statement
Answer:
Point
Step-by-step explanation:
once two line intersect the area where they intersected becomes a point
5) Suppose a slice of a 12-inch pizza has an area of 20 square inches. What is the angle of
this slice?
Answers
Answer:
The angle of slice is approximately 16°.
Step-by-step explanation:
The slice of pizza represent the sector of a circle.
The area of a sector is:
[tex]A=\frac{1}{2}r^{2}\phi[/tex]
Here,
r = radius of the circle
Φ = angle in radians
Given:
A = 20 inches²
r = 12 inch
Compute the angle of the slice as follows:
[tex]A=\frac{1}{2}r^{2}\phi[/tex]
[tex]\phi=\frac{2\times A}{r^{2}}[/tex]
[tex]=\frac{2\times 20}{12\times 12}\\\\=0.2778[/tex]
The angle us 0.2778 radians.
Convert the angle into degrees as follows:
[tex]\text{Angle}=0.2778\times\frac{180}{\pi}=15.9168\approx 16^{o}[/tex]
Thus, the angle of slice is approximately 16°.
Solve the following linear equation and explain how you did it 1.1z+5.5=2.2z
Answers
Answer:
z = 5
Step-by-step explanation:
1.1z+5.5=2.2z
Subtract 1.1z from each side
1.1z-1.1z+5.5=2.2z-1.1z
5.5 = 1.1z
Divide each side by 1.1
5.5/1.1 = 1.1z/1.1
5 = z
helpppppp asappppp plsssss
Answers
Answer:
x = -2
Step-by-step explanation:
The segments described in the question are equidistant (meaning they are the same length). Therefore, using algebraic techniques, we can set these two equal to each other and solve for x.
4x - 8 = 6x - 4 Combine like terms by subtracting 6x from both sides.
-2x - 8 = -4 Combine like terms by adding 8 to both sides.
-2x = 4 Divide by -2 on both sides of the equation.
x = -2
How to Write the numbers 0.253 in two other forms
Answers
Answer:
253/1000, 23.5%
Step-by-step explanation:
Find the percent of increase to the nearest whole from 12 to 20
Answers
Answer:
The answer is
[tex]67\%[/tex]Step-by-step explanation:
To find the percentage increase we use the formula
[tex]Percentage \: change = \frac{change}{original \: \: quantity} \times 100\%[/tex]From the question
The original value = 12
To find the change we subtract the smaller value from the larger one
That's
Change = 20 - 12 = 8
So the percentage increase is
[tex] \frac{8}{12} \times 100 \%\\ = \frac{2}{3} \times 100\% \\ = 66.67\%[/tex]We have the final answer as
[tex]67\%[/tex] to the nearest whole number
Hope this helps you
Wich expression is equivalent to 0.33b+b+0.31b?
A.b+0.64
B.1.64b
C.1.02b
D.1+0.64b
Answers
Answer:
B. 1.64b
Step-by-step explanation:
0.33b+1b+0.31b
=1.64b
The U.S. Census Bureau would like to estimate the average square footage of a new single-family home with a 95% confidence interval and a margin of error within plus or minus 100 square feet. Assuming the standard deviation for the square footage of new single-family homes is 850 square feet, the required sample size is ________.
Answers
Answer:
The sample size is [tex]n =278[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 100[/tex]
The standard deviation is [tex]\sigma = 850[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100-95)\%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = \frac{(Z_{\frac{\alpha }{2}})^2}{E^2} * \sigma^2[/tex]
=> [tex]n = \frac{(1.96)^2}{100^2} * 850^2[/tex]
=> [tex]n =278[/tex]
Find the measure of x.
A. 90
B. 47
C. 43
D. 53
Answers
Answer:
C. 43
Step-by-step explanation:
Use of theorem:An angle inscribed across a circle's diameter is always a right angleAs per above:
x + 47 = 90x = 90 -47 x = 43Correct answer choice is C. 43
Answer:
C.) 43
Step-by-step explanation:
I got it right on founders edtell
A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. : : What type of test is being conducted in this problem?
Answers
Complete question is;
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
H0: μ = 4
H1: μ > 4
What type of test is being conducted in this problem? What parameter is being tested?
Answer:
Type of test = right tailed
Parameter being tested = population mean
Step-by-step explanation:
We are given the null and alternative hypothesis as;
H0: μ = 4
H1: μ > 4
Now, let's define terms;
The right tailed test and the left tailed test are both examples of one-tailed tests. This is because the area where we would reject the null hypothesis is only in one tail. Which means that in the case of left tail, the rejection region will occur only to the left of the graph while for the right tail, the rejection region will occur only to the right of the graph.
Whereas, for two tailed test, the area where we would reject the null hypothesis would not just be in one tail or one side of the graph but could be in either tail or either side of the graph. Hence, the name "two - tail".
Now, applying this to the question, the alternative hypothesis says the mean is greater than 4. On, a graph, an increase in number on the x-axis means going to the right. Thus, it is a right tailed test
Now, the sample being tested is population mean because in statistics, the symbol μ is generally used to denote population mean.
calculate the length of the altitude of an iso scales triangle whose equal sides are 13cm long with a base 24cm
Answers
Answer:
5 cm
Step-by-step explanation:
13² - 12² = x²
169 - 144 = x²
25 = x²
5 = x
Describe the mental math steps you would use to find 7(42) (this is the distributive property by the way. :] )
Answers
Answer:
multiply 7 by 42
= 294
42 x 7 can be done as mental math, but that is challenging for some people.
Answer: 294
Break up 42 like so: 42 = 40 + 2
Then we can say,
7*(42) = 7*(40+2) = 7*40 + 7*2 = 280 + 14 = 294
The mental math part is knowing that 7*4 = 28, then you add on a zero to get 7*40 = 280. This is added to 7*2 = 14 to get the final answer above.
The spinner below shows 5 equally sized slices. Tammy spun the dial 25 times and got the following results. Fill in the table below. Round your answers to the nearest thousandths.
Answers
Answer:
a) 4/25, or 0.16, or 16%
b) 1/5, or 0.2, or 20%
c) The first option - the theoretical and experimental values should become closer the more trials that are performed.
Step-by-step explanation:
a) 4 of Tammy's 25 spins landed on black, so the experimental probability is 4/25, or 0.16, or 16%.
b) The spinner is split into 5 equal sections. Assuming it is fair, the chance of landing in any given section for a single spin is 1/5, or 0.2, or 20%.
c) The theoretical and experimental values should get closers the more trials you do.
For example, consider 1 coin flip vs 100. The theoretical probability of landing on a given side of a coin is 1/2, or 0.5, or 50%. With a single flip, your experimental probability will either be 0% or 100%, both off of the theoretical probability by 50%. After 100 flips however, the experimental and theoretical probabilities will be much closer to each other.
I need help please for the answer and how to solve it
Answers
Answer:
32) a) x = 3/19 ounces
33) d) 0,2 meter per minute
Step-by-step explanation:
32)
7 1/2 = 15/2
47 1/2 = 95/2
95/2 dough 15/2 sugar
1 dough x = (15/2*1) / 95/2
x = (15/2)(95/2)
x = 15/95
x = 3/19 ounces
33)
Distance 16 | 18 | 20 | 22
Time 80 | 90 | 100 | 110
Time 90 - 80 = 10
Distance 18 - 16 = 2
Each 10 minutes go 10 meters
2 / 10 = 0,2 meter per minute
how to answer the (a) question?
help please
Answers
i believe its 4
Step-by-step explanation:
Kadir, Chandran and Ping Wei participated in a Science quiz. The number of questions they had answered was in the ratio 4:6:3. Chandran had answered 30 questions. Calculate the total number of questions Kadir amd Ping Wei had answered.
Answers
Answer:
35
Step-by-step explanation:
We can call the amount of questions they answered as 4x, 6x and 3x respectively. Since Chandran answered 30 questions, we know that 6x = 30 so x = 5. The total number of questions Kadir and Ping Wei answered was 4x + 3x = 7x and since we know that x = 5, the answer is 7 * 5 = 35 questions.
Solve for x: three halves plus one half times x equals two x x equals two thirds x = 1 x = 2 x = 3
Answers
Answer:
x=1
Step-by-step explanation:
because 3 over 2 plus 1 over 2 is 4 over 2 and 2 fits in 4 2 times so its 2 x but since thats solving for 2 half of that is 1, thus its x=1
The required simplified value of x is x = 1. Option 1 is correct.
Given,
Three halves plus one-half times x equals two x.
To simplify the above expression.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3/2 + 1/2 x = 2x
3/2 = 2x - 1/2 x
3x / 2 = 3 / 2
x = 1
Thus, the required simplified value of x is x = 1. Option 1 is correct.
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In an examination of purchasing patterns of shoppers, a sample of 36 shoppers revealed that they spent, on average, $50 per hour of shopping. Based on previous years, the population standard deviation is $4.80 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, calculate a 90% confidence interval.
Answers
Answer:
the 90% confidence interval is ( 48.684 , 51.316 )
Step-by-step explanation:
Given that :
the sample size = 36
Sample Mean = 50
standard deviation = 4.80
The objective is to calculate a 90% confidence interval.
At 90% confidence interval ;
the level of significance = 1 - 0.9 = 0.1
The critical value for [tex]z_{\alpha/2} = z_{0.1/2}[/tex]
[tex]= z_{0.05}[/tex] = 1.645
The standard error S.E = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
=[tex]\dfrac{4.8}{\sqrt{36}}[/tex]
[tex]=\dfrac{4.8}{6}[/tex]
= 0.8
The Confidence interval level can be computed as:
[tex]\bar x \ \pm z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
For the lower limit :
[tex]\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
[tex]=50 \ - 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}[/tex]
[tex]=50 \ - 1.645 \times \ 0.8 }}[/tex]
=50 - 1.316
= 48.684
For the upper limit :
[tex]\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}[/tex]
[tex]=50 \ + 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}[/tex]
[tex]=50 \ + 1.645 \times \ 0.8 }}[/tex]
=50 + 1.316
= 51.316
Thus, the 90% confidence interval is ( 48.684 , 51.316 )
Simplify the expression:
(10x2 -1 + 4x) + (3 + 5x2 - 4x)
Answers
Answer:
15x^2+2
Step-by-step explanation:
(10x^2 -1 + 4x) + (3 + 5x^2 - 4x)
Combine like terms
10x^2+5x^2+4x-4x-1+3
15x^2+2
plz solve it.anyone
Answers
Answer:
See below.
Step-by-step explanation:
1i
75 = 3 * 5^2
Multiply by 3
1ii
112 = 2^4 * 7
Multiply by 7
1iii
128 = 2^7
Multiply by 2
1iv
243 = 3^5
Multiply by 3
1v
392 = 2^3 * 7^2
Multiply by 2
A long distance runner can run 2 miles every 17 minutes. At this rate how ling would it take the runner to run 16 miles.
Answers
Answer:
136 minutes
Step-by-step explanation:
Given :
2 miles ----> takes 17 min
1 mile -----> takes 17/2 min
hence the unit rate is (17/2) min per mile
Thus, 16 miles will take
= (17/2) miles per min x 16 miles
= (17/2) x 16
= 136 minutes
Answer:
136 min
Step-by-step explanation:
lets make it simple.
2 miles / 17 min = 16 miles / x
just cross multiply
2 x = 17 (16)
2 x = 272
x = 272 / 2
x = 136 min
7/25 divided by 3/5 as a fraction
Answers
Answer:
[tex] \frac{7}{15} [/tex]
Step-by-step explanation:
[tex] \frac{7}{25} \div \frac{3}{5} = \frac{7}{25} \times \frac{5}{3} = \frac{35}{75} = \frac{7}{15} [/tex]
Hope this helps ;) ❤❤❤
The calculated division of the numbers 7/25 divided by 3/5 is 7/15
How to calculate the division of the numbersFrom the question, we have the following parameters that can be used in our computation:
7/25 divided by 3/5
When represented as an equation, we have
7/25 divided by 3/5 = 7/25 ÷ 3/5
Represent as a product expression
So, we have
7/25 divided by 3/5 = 7/25 * 5/3
So, we have the following result
7/25 divided by 3/5 = 7/15
Using the above as a guide, we have the following:
the result is 7/15
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the sum of twice a number and 15 less than the number is the same as the difference between -19 and the number. What is the number?
Answers
Answer:
-1
Step-by-step explanation:
Twice a number: 2n.
15 less than the number: n-15.
The sum of those: (2n) +(n-15) = 3n-15.
__
The difference between -19 and the number: -19-n
__
These values are the same, so we have ...
3n -15 = -19 -n
4n = -4 . . . . . . . . add n+15 to both sides
n = -1 . . . . . . . . . divide by -4
The number is -1.
Ms. Ironperson and Mr. Thoro are making Avenger posters to give children when they visit Avenger Academy. Ms. Ironperson has completed 12 posters and will complete 6 more per day. Mr. Thoro has not started yet but can make 12 per day. At some point Mr. Thoro will catch up and both will have finished the same number of posters. When this does happen, how many posters will each Avenger have completed? If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?
Answers
Answer:
1) When this does happen, how many posters will each Avenger have completed?
24 posters each.
2) If x denotes the number of days and y denotes the number of posters, what are the equations needed to solve this problem?
y = 12 + 6x.......... Equation 1
y = 12x .......... Equation 2
Step-by-step explanation:
1) When this does happen, how many posters will each Avenger have completed?
We are told in the question:
Number of days = x
Number of posters = y
Ms. Ironperson has completed 12 posters and will complete 6 more per day.
y = 12 + 6x.......... Equation 1
Mr. Thoro has not started yet but can make 12 per day.
y = 12x................Equation 2
Hence, the equations needed to solve this problem:
y = 12 + 6x.......... Equation 1
y = 12x .......... Equation 2
We substitute 12x for y in equation 1
y = 12 + 6x.......... Equation 1
12x = 12 + 6x
Collect like terms
12x - 6x = 12
6x = 12
x = 12/6
x = 2
Hence, since x = the number of days,
The number of days = 2 days
Substitute 2 for x in Equation 2
y = 12x .......... Equation 2
y = 12 × 2
y = 24 posters.
Since y = number of posters,
number of posters = 24 posters.
We were told in the question that, when Mr Thoro catches up with Ms Ironperson, that would both have completed the same number of posters.
Hence, both Avengers would have completed 12 posters each.
what is refraction
Answers
Answer:
I hope this will be the answer... ✌️
[tex]\large{\pmb{\underline{\underline{\sf{Refraction:-}}}}}[/tex]
Refraction is the bending of a light or sound wave, or the way the light bends when entering the eye to form an image on the retina.
[tex]\large{\pmb{\underline{\underline{\sf{Examples~ Of~ Refraction:-}}}}}[/tex]
Bending of the sun's rays as they enter raindrops, forming a rainbow.[tex]{\huge{\underline{\small{\mathbb{\pink{HOPE \ THIS \ HELPED \ UH:)}}}}}}[/tex]
Cheers !! :3
Solve the equation for X 3(x+2)=2(2-x)
Answers
Answer:
x = - 2/5Step-by-step explanation:
[tex]3(x+2)=2(2-x)\\\\\mathrm{Expand\:}3\left(x+2\right):\quad 3x+6\\\\\mathrm{Expand\:}2\left(2-x\right):\quad 4-2x\\\\3x+6=4-2x\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\3x+6-6=4-2x-6\\\\3x=-2x-2\\\\\mathrm{Add\:}2x\mathrm{\:to\:both\:sides}\\\\3x+2x=-2x-2+2x\\\\Simplify\\\\5x=-2\\\\Divide\:both\:sides\:by5\\\\\frac{5x}{5}=\frac{-2}{5}\\\\x=-\frac{2}{5}[/tex]
Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = x2 y = 6x − x2
Answers
Answer:
81π for the x axis.
Step-by-step explanation:
STEP ONE: Determine the intersection.
we are given from the question that y = x^2 and y = 6x − x^2. Therefore if y = x^2, then we will have;
x^2 = 6x - x^2 ---------------------------------------------------------------------------------[1].
Solving and factorizing the equation [1] above give us x = 0 and x = 3 (that is x[6 -2x] = 0 ). Therefore, the point of intersection = (0,0) and (3,9).
STEP TWO: Determine the value for the cross sectional area.
The cross sectional area= [6x - x^2]π - [x2]^2 π. --------------[2].
The cross sectional area = -12 π[x -3]x^2.
STEP THREE: integrate the cross sectional area taking x =3 and x =0 as the upper and lower integration limits or boundaries with respect to dx to determine the vome in the x axis.
volume =∫-12 π[x -3]x^2 dx.volume = -12 π[ (3)^4/4 - (3)^3 ] = 81π.volume, v with respect to the x axis = 81π