Step-by-step explanation:
sin∠M = cos∠N
sin∠M = cos(30°)
sin∠M = √3 / 2
m∠M = 60° or 120°
If ∠M is acute, m∠M = 60°.
Answer: The measure of ∠M is 60°
Step-by-step explanation:
The complement of 30° is 60°
sin∠M =cos∠N
sin∠60°=cos∠30°
the measure of ∠M is 60°
Which expression is equivalent to 73 ⋅ 7−5? 72 77 1 over 7 to the 2nd power 1 over 7 to the 7th power
Answer:
1/7^2
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
__
Then your expression simplifies to ...
[tex]7^3\cdot 7^{-5}=7^{3-5}=7^{-2}=\boxed{\dfrac{1}{7^2}}[/tex]
Answer:
The answer is 1/7^2
Step-by-step explanation:
I took the test lol
A research center claims that % of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of adults in that country, % say that they would travel into space on a commercial flight if they could afford it. At , is there enough evidence to reject the research
Complete Question
A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At , is there enough evidence to reject the research center's claim
Answer:
Yes there is sufficient evidence to reject the research center's claim.
Step-by-step explanation:
From the question we are told that
The population proportion is p = 0.30
The sample proportion is [tex]\r p = 0.34[/tex]
The sample size is n = 700
The null hypothesis is [tex]H_o : p = 0.30[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.30[/tex]
Here we are going to be making use of level of significance = 0.05 to carry out this test
Now we will obtain the critical value of [tex]Z_{\alpha }[/tex] from the normal distribution table , the value is [tex]Z_{\alpha } = 1.645[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \r p - p }{ \sqrt{ \frac{ p (1-p)}{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.34 - 0.30 }{ \sqrt{ \frac{ 0.30 (1-0.30 )}{ 700} } }[/tex]
[tex]t = 2.31[/tex]
Looking at the values of t and [tex]Z_{\alpha }[/tex] we see that [tex]t > Z_{\alpha }[/tex] hence the null hypothesis is rejected
Thus we can conclude that there is sufficient evidence to reject the research center's claim.
Consider population data with μ = 30 and σ = 3. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean. Lower Limit Upper Limit
Answer:
A. 10%
B. Lower limit= 21
Upper limit = 39
Step-by-step explanation:
Mean = 30
SD = 3
a. COV = SD/|x| × 100
= 3/30 × 100
= 10%
= 0.1
B. For 88.9 chevbychev interval:
= (1 - 1/K²) = 0.889
= 1/K² = 1 - 0.889
= 1/K² = 0.111
= K² = 1/0.111
= K² = 9
= K = √9
K = 3
Lower limit = 30 - 3(3)
Lower limit = 21
Upper limit = 30 + 3(3)
Upper limit = 39
Therefore lower limit is 21 and upper limit is 39
The value of 3 in 783.97
Answer:
place value of 3 in 783.97 is 3
Step-by-step explanation:
Answer:
Units
Step-by-step explanation:
The units start counting from 3 because after the point that is the 9 start counting tenth
Salaries of 42 college graduates who took a statistics course in college have a mean, , of . Assuming a standard deviation, , of $, construct a % confidence interval for estimating the population mean .
Answer:
The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
Step-by-step explanation:
The complete question is:
Salaries of 42 college graduates who took a statistics course in college have a mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard deviation, σ of $10,016 construct a 99% confidence interval for estimating the population mean μ.
Solution:
The (1 - α)% confidence interval for estimating the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
The critical value of z for 99% confidence interval is:
[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]
Compute the 99% confidence interval for estimating the population mean μ as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]
Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
which of the following best describes the bases of a cylinder? A. Congruent B. Polygons C. Parallel D. Discs (Check All That Apply)
Answer:
A. Congruent and D. Discs
Step-by-step explanation:
You won't see a cylinder that doesn't have congruent bases
Look at the shape of the bases and look at a disc compare their shape
We can describe the bases of a cylinder as congruent.
What is the volume of cylinder?The volume of cylinder is given by -
V = πR²h
Given is to describe the bases of a cylinder.
The cylinders are uniform in cross - section. Therefore, the bases of the cylinder will have the same area. So, we can conclude that the given bases are congruent.
Therefore, we can describe the bases of a cylinder as congruent.
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Which statements about the dilation are true? Check all that apply. Triangle X prime Y prime Z prime. Point X prime is 2 units from the center of dilation C and point Z prime is 3 units from the center of dilation. Triangle X Y Z. Point X is 5 units from point C and point Z is 7.5 units from point C. The center of dilation is point C. It is a reduction. It is an enlargement. The scale factor is 2.5. The scale factor is Two-fifths.
Answer:
I only know two right answers.
A: The center of dilation is point C.
C: It is an enlargement.
E: The scale factor is 2/5.
Step-by-step explanation:
These two answers are correct because When you look in the center you see a C.
You tell if it is a reduction because the pre image is small but the image is big.
The center of dilation is point C.
It is an enlargement.
The scale factor is 2/5
The correct options are D, F, H.
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
Given:
The transformation of the figure is dilation.
The figure is given in the attached image.
From the diagram:
The center of dilation is point C.
It is an enlargement.
The scale factor is 2/5
Therefore, all the correct statements are given above.
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The dot plot represents a sampling of ACT scores: dot plot titled ACT Scores with Score on the x axis and Number of Students on the y axis with 1 dot over 24, 3 dots over 26, 3 dots over 27, 5 dots over 28, 3 dots over 30, 3 dots over 32, 1 dot over 35 Which box plot represents the dot plot data? box plot titled ACT Score with a minimum of 24, quartile 1 of 25, median of 26, quartile 3 of 29, and maximum of 35 box plot titled ACT Score with a minimum of 23, quartile 1 of 25, median of 26, quartile 3 of 29, and maximum of 36 box plot titled ACT Score with a minimum of 23, quartile 1 of 27, median of 30, quartile 3 of 34, and maximum of 36 box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35
Answer:
box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35
Step-by-step explanation:
The scores of the students represented on the dot plot are:
1 dot => 24
3 dots => 26, 26, 26
3 dots => 27, 27, 27
5 dots => 28, 28, 28, 28, 28
3 dots => 30, 30, 30
3 dots => 32, 32, 32
1 dot => 35
Quickly, we can ascertain 3 values from these data points of which we can use to find out which box plot represents the dot plot data.
The minimum score = 24
The maximum score = 35
The median score is the 10th value, which is the middle value of the data point = 28
Therefore, we can conclude that: "box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35".
find the area of square whose side is 2.5 cm
Answer:
6.25
Step-by-step explanation:
2.5 *2.5=6.25
Answer:
6.25cm^2.
Step-by-step explanation:
To find the area of a square, you multiply the two sides, 2.5✖️2.5.
This gives the area of 6.25cm^2.
Hope this helped!
Have a nice day:)
If tanA = 3
evaluate
CosA + sinA\
casA - SinA
Answer:
Hi, there!!!
I hope you mean to evaluate cosA+ sonA /cosA - sinA.
so, i hope the answer in pictures will help you.
What is the simplified form of the following expression? 2 StartRoot 18 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 162 EndRoot 6 StartRoot 2 EndRoot 18 StartRoot 2 EndRoot 30 StartRoot 2 EndRoot 36 StartRoot 2 EndRoot
Answer:
[tex]18\sqrt2[/tex]
Step-by-step explanation:
To simplify:
[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 }[/tex]
First of all, let us write 18 and 162 as product of prime factors:
[tex]18 = 2 \times \underline{3 \times 3}\\162 = 2 \times \underline{3 \times 3} \times \underline{3 \times 3}[/tex]
The pairs are underlined as above.
While taking roots, only one of the numbers from the pairs will be chosen.
Now, taking square roots.
[tex]\sqrt{18} =3 \sqrt2[/tex]
[tex]162 = 3 \times 3 \times \sqrt 2 = 9 \sqrt2[/tex]
So, the given expression becomes:
[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 } = 2 \times 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}[/tex]
So, the answer is:
[tex]18\sqrt2[/tex] or 18 StartRoot 2 EndRoot
Answer:
its B. 18 sqrt(2)
Step-by-step explanation:
just took test
88 feet/second = 60 miles/hour. How many feet per second is 1 mile/hour? (Hint: divide both sides of the equation
by the same amount.)
Round to the nearest thousandth.
One mile per hour is equivalent to
ao feet/second
Time
(minutes)
Water
(gallons)
1
16.50
1.5
24.75
2
33
find the constant of proportionality for the second and third row
Answer:
16.50
Step-by-step explanation:
Constant of proportionality = no of gallons of water per 1 minute.
In the first row, we have 16.50 gallons of water per 1 minute.
In the 2nd row, we have 24.75 gallons of water in 1.5 minutes. In 1 minute, we will have 24.75 ÷ 1.5 = 16.50 gallons
In the 3rd row, we have 33 gallons in 2 minutes. In 1 minute, we will have 33 ÷ 2 = 16.50 gallons.
We can see that there seems to be the same constant of proportionality for the 2nd and 3rd row, which is 16.50.
Thus, a relationship between gallons of water (w) and time (t), considering the constant, 16.50, can be written as: [tex] w = 16.50t [/tex]
This means the constant of proportionality, 16.50, is same for all rows.
Max believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 5 days. Below you are given the results of the sample.
Cups of Coffee Sold Temperature
350 50
200 60
210 70
100 80
60 90
40 100
A. Which variable is the dependent variable?
B. Compute the least squares estimated line.
C. Compute the correlation coefficient between temperature and the sales of coffee.
D. Predict sales of a 90 degree day.
Answer:
1. cups of coffee sold
2.Y = 605.7 - 5.943x
3. -0.952
4. 70.84
Step-by-step explanation:
1. the dependent variable in this question is the cups of coffee sold
2. least square estimation line
Y = a+bx
we have y as the cups of coffee sold
x as temperature.
first we will have to solve for a and then b
∑X = 450
∑Y = 960
∑XY = 61600
∑X² = 35500
∑Y² = 221800
a = ∑y∑x²-∑x∑xy/n∑x²-(∑x)²
a = 960 * 35500-450*61600/6*35500-450²
a = 6360000/10500
= 605.7
b = n∑xy - ∑x∑y/n∑x²-(∑x)²
= 6*61600 - 450*960/6*35500 - 450²
= -5.943
the regression line
Y = a + bx
Y = 605.7 - 5.943x
3. we are to find correlation coefficient
r = n∑xy - ∑x∑y multiplied by√(n∑x²-(∑x)² * (n∑y² - (∑y)²)
= 6*61600 -960*450/√(6*35500 - 450²)*(6*221800 - 960²)
=-62400/√4296600000
= -62400/65548.5
= -0.952
4. we have to predict sales of a 90 degree day fro the regression line
Y = 605.7 - 5.943x
y = 605.7 - 5.943(90)
y = 605.7 - 534.87
= 70.84
Bianca took a job that paid $150 the first week. She was guaranteed a raise of 6% each week. How much money will she make in all over 8 weeks? Round the answer to the nearest cent. please answer with the reasoning, I want to learn how to solve this and not just get the answer. Thank you.
Answer:
$225.54 (hope it help)
Step-by-step explanation:
for 2nd week
$150 for the first week and a raise of 6% each week
which means 150+6%
6% of 150 is 9 (150x0.06)
150+9=159
and it repeats
for 3rd week
6% of 159 is 9.54 (159x0.06)
159+9.54=168.54
for 4th week
6% of 168.54 is 10.1124 (168.54x0.06)
168.54+10.1124=178.652
for 5th week
6% of 178.652 is 10.71912 (178.652x0.06)
178.652+10.71912=189.37112
an easier to do it is to just do 178.652 + 6% on your calculater
and I'll skip all the way to the 8th since you know the formula
212.777390432+6%=225.544033858
225.544033858≈225.54
PLEASE HELP ASAP RN!!!!!!
Answer:
3sqrt(2)
Step-by-step explanation:
sqrt(32) - sqrt(2)
rewriting sqrt(32)
sqrt(16*2) - sqrt(2)
sqrt(16) * sqrt(2) - sqrt(2)
4 sqrt(2) - sqrt(2)
3sqrt(2)
What is the domain of the set of ordered pairs?
(8, -13); ( 0,-5); (4, -9); (-3,2)
The domain is the input values, which are the x values.
The x values in the given pairs are: 8, 0,4,-3
The domain set is (-3, 0, 4, 8)
The required domain of the set of ordered pairs is [8, 0, 4, -3]
Given that,
Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).
We have to determine,
The domain of the set of ordered pair.
According to the question,
The domain refers to the set of possible input values.
The domain of a graph consists of all the input values shown on the x-axis.
A relation is a set of ordered pairs.
The domain is the set of all the first components of the ordered pairs.
Then,
Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).
Here, Set of all the input values on the x-axis.
Therefore,
The set of values of x is { 8,0,4,-3 }
Hence, The required domain of the set of ordered pairs is [8, 0, 4, -3]
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Translate this sentence into an equation. 43 is the sum of 11 and Carlos age. Use the variable c to represent Carlos age.
Answer:
c + 11 = 43
Step-by-step explanation:
C = Carlos age
11 = The number added
43 = The number added plus carlos' age
c +11 = 43
c = 43 - 11
c = 32
Carlos' age is 32 years.
Answer:
C+11=43
Step-by-step explanation:
C= Carlos age
11= added number
43= Carlos age +added number
C+11=43
C=43-11
C=32
Age of Carlos 32. :)
Lines a and b are parallel. If the slope of line a is , what is the slope of line b?
A.
-
B.
4
C.
D.
-4
Answer:
C. 1/4
Step-by-step explanation:
Parallel lines always have the same slope.
Answer:
C. 1/4
Step-by-step explanation:
Parallel lines have the same slope. If line b is parallel to line a, and line a has slope 1/4, then line b has slope 1/4.
If a recipe which makes 8 servings calls for 2 cups of sugar, how many cups of sugar will it take to make 18 servings?
Answer:
4.5
Step-by-step explanation:
2/8=x/18
Answer:
4.5 cups
Step-by-step explanation:
first you set up the problem like servings/cups. This would look like 8/2. Then you add the 18 servings and make it a cross multiplication problem. The expression would look like 8/2=18/x. You cross multiply and get 8x=36. Divide by 8 and get x=4.5 cups.
solve for x: -3(x + 1)= -3(x + 1) - 5
Answer:
No solution : 0= -5Step-by-step explanation:
[tex]-3\left(x+1\right)=-3\left(x+1\right)-5\\\\\mathrm{Add\:}3\left(x+1\right)\mathrm{\:to\:both\:sides}\\\\-3\left(x+1\right)+3\left(x+1\right)=-3\left(x+1\right)-5+3\left(x+1\right)\\\\\mathrm{Simplify}\\\\0=-5\\\\\mathrm{The\:sides\:are\:not\:equal}\\\\\mathrm{No\:Solution}[/tex]
I NEED this answered within the next 30 minutes! Please it is simple. There is an error in this. What is it?
Answer:
(a). x = 80°
(b). x = 7.2 units
Step-by-step explanation:
Angle formed between the tangents from a point outside the circle measure the half of the difference of intercepted arcs.
(a). Here the intercepted arcs are,
Measure of major arc = 360° - 100°
= 260°
Measure of minor arc = 100°
x° = [tex]\frac{1}{2}[m(\text{Major arc})-m(\text{Minor arc})][/tex]
= [tex]\frac{1}{2}(260-100)[/tex]
x = 80°
(b). If a secant and tangent are drawn form a point outside the circle, then square of the measure of tangent is equal to the product of the measures of the secant segment and and its external segment.
x² = 4(4 + 9)
x² = 4 × 13
x² = 52
x = √52
x = 7.211 ≈ 7.2 units
Find the interest on a Principal Balance of $10,000 over the course of eight years with an interest rate of 5.5%. Do this for: Simple Interest.
Answer:
Simple Interest : $ 4400
Step-by-step explanation:
We want to calculate the interest on $ 10,000, at 5.5% interest rate per year, over a course of 8 years.
We can use the simple interest formula here, or :
I = P × r × t,
Where P is the principle amount, $ 10,000, r is the interest rate, 5.5% each year, or in decimal form 5.5 / 100 = 0.055. t is the time, 8 years.
Simple Interest : 10000 × 0.055 × 8 = $4400.00
Then again the interest can be added to the principal amount ( $10,000 ) to receive some new amount after 8 years, which is $ 14,000. However the simple interest earned in 8 years at a rate of 5.5% should be $4400.
The simple interest earned on the amount is $4,400
Interest is the total amount that would be paid or earned from making an investment or taking a loan over a period of time.
Simple Interest = principal x time x interest rate
principal = amount borrowed = $10,000
time = 8 years
Interest rate = 5.5%
10,000 x 0.055 x 8 = $4,400
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Let X denote the day she gets enrolled in her first class and let Y denote the day she gets enrolled in both the classes. What is the distribution of X
Answer:
X is uniformly distributed.
Step-by-step explanation:
Uniform Distribution:
This is the type of distribution where all outcome of a certain event have equal likeliness of occurrence.
Example of Uniform Distribution is - tossing a coin. The probability of getting a head is the same as the probability of getting a tail. The have equal likeliness of occurrence.
Allison bought jelly beans to share with her friends. She bought pounds of blueberry jelly beans and pounds of lemon jelly beans. If she gave pounds of jelly beans away to her friends, how many pounds of jelly beans does Allison have left?
Answer: [tex]1\dfrac{11}{12}\text{ pounds}[/tex]
Step-by-step explanation:
The complete question is provided in the attachment.
Given, Amount blueberry jelly beans= [tex]1\dfrac{1}{4}[/tex] pounds
[tex]=\dfrac{5}{4}[/tex] pounds.
Amount lemon jelly beans = [tex]2\dfrac{1}{3}[/tex]pounds
[tex]=\dfrac{7}{2}[/tex] pounds
Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans
[tex]=(\dfrac{5}{4}+\dfrac{7}{3})[/tex] pounds
[tex]=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}[/tex]
Amount of jelly beans she gave away = [tex]1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}[/tex]
Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away
=[tex]\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}[/tex]
She has left [tex]1\dfrac{11}{12}\text{ pounds}[/tex] of jelly beans.
The cost of a daily rental car is as follows: The initial fee is $39.99 for the car, and it costs $0.20 per mile. If Julie's final bill was $100.00 before taxes, how many miles did she drive?
Answer:
300.05 miles
Step-by-step explanation:
initial fee= $39.99
final bill = $ 100
cost =$ 0.20 per mile
remaining amount = $ 60.01
solution,
she drive = remaining amount / cost
=60.01/0.20
=300.05 miles
Answer:
500 miles
Step-by-step explanation:
Let us use cross multiplication to find the unknown amount.
Given:
1) Cost for 1 mile=$0.20
2)Cost for x miles=$100
Solution:
No of miles Cost
1) 1 $0.20
2)x $100
By cross multiplying,
100 x 1= 0.20x
x=100/0.20
x=500 miles
Thank you!
two ratios equivalent to 27:9
Answer:
Those ratios could be 3:1
Please help. I’ll mark you as brainliest if correct!
Answer:
9 3 -7 -13
4 -4 11 8
0 9 2 -4
Step-by-step explanation:
9 3 -7 -13
4 -4 11 8
0 9 2 -4
Answer: 9 3 -7 -13
4 -4 11 8
0 9 2 -4
Step-by-step explanation:
Simply. Who ever answers this will be marked Brainlist.
Answer:
Step-by-step explanation:
Hello,
[tex]r^3s^{-2}\cdot 8r^{-3}s^4\cdot 4rs^5\\\\=r^{3-3+1}s^{-2+4+5}\cdot 8\cdot 4\\\\\boxed{=32\cdot r\cdot s^7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
|5x|=3 please help me
