Answer:
Cos²(45°—A) + cos²(45°+A)
= [2 cos²(45°—A) + 2 cos²(45°+A)] /2
= [{2 cos²(45°—A)—1} + {2 cos²(45°+A)—1} + 2] /2
= [cos2(45°—A)+cos2(45°+A)+2]/2
= [cos(90°—2A)+cos(90°+2A)+2]/2
= (sin2A—sin2A+2)/2
= 2/2
= 1
Determine the measure of x? Please include the way you got the answer as well please
Answer:
x = 16°
Step-by-step explanation:
The three internal angles of the triangle are:
180° - 91° = 89° (angles in a straight line)
180° - 105° = 75° (angles on a straight line)
x = x (vertical angles are congruent)
x + 89 + 75 = 180 (sum of interior angles of a ∆)
x + 164 = 180
x = 180 - 164 (subtraction property of equality)
x = 16°
HELP ASAP WILL GIVE BRAINLEIST
Answer:
X=8 1/13
Y=31 11/13
Step-by-step explanation:
Answer:
x = 15
y = 63
Step-by-step explanation:
[tex](9x - 7) \degree + (4x - 8) \degree = 180 \degree \\ (linear \: pair \: \angle s) \\ \\ (9x - 7 + 4x - 8) \degree = 180 \degree \\\\ (13x - 15) \degree = 180 \degree \\ \\ 13x - 15 = 180 \\ \\ 13x = 180 + 15 \\ \\ 13x = 195 \\ \\ x = \frac{195}{13} \\ \\ x = 15 \\ \\ (2y + 2) \degree = (9x - 7) \degree \\ (interior \: alternate \: \angle s) \\ \\ (2y + 2) \degree = (9 \times 15 - 7) \degree\\ \\ (2y + 2) \degree = (135- 7) \degree\\ \\ (2y + 2) \degree =128 \degree \\ \\ 2y + 2 = 128 \\ \\ 2y = 128 - 2 \\ \\ 2y = 126 \\ \\ y = \frac{126}{2} \\ \\ y = 63[/tex]
math question???????????????????
please help ??????
Will mark brainliest
Answer: a=54
Step-by-step explanation:
2a = (a+10) +44
2a=a+10+44
2a=a+54
a=54
Assume that you have a sample of n1=9, with the sample mean X1=46, and a sample standard deviation of S1=4, and you have an independent sample of n2=12 from another population with a sample mean of X2=31 and the sample standard deviation S2=5. Complete parts (a) through (d) below. a. What is the value of the pooled-variance tSTAT test statistic for testing H0: μ1=μ2? tSTAT=nothing (Round to two decimal places as needed.) b. In finding the critical value, how many degrees of freedom are there? nothing degrees of freedom (Simplify your answer.) c. Using a significance level of α=0.1, what is the critical value for a one-tail test of the hypothesis H0: μ1≤ μ2 against the alternative H1: μ1>μ2? The critical value is nothing. (Round to two decimal places as needed.) d. What is your statistical decision? A. Reject H0 because the computed tSTAT test statistic is greater than the upper-tail critical value. B. Reject H0 because the computed tSTAT test statistic is less than the upper-tail critical value. C. Do not reject H0 because the computed tSTAT test statistic is less than the upper-tail critical value. D. Do not reject H0 because the computed tSTAT test statistic is greater than the upper-tail critical value.
Answer:
a. t`= 7.63
b.υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
= 18.885 ≈19 The degrees of freedom is always rounded in this calculation.
c. The critical region for one tailed test for alpha= 0.1 and 19 degrees of freedom is 1.328= 1.33
The critical region is ║t║` ≥ t 0.05,19 = 1.729= 1.73
A. Reject H0 because the computed tSTAT test statistic is greater than the upper-tail critical value
Step-by-step explanation:
Answer:
Step-by-step explanation:
We state our null and alternative hypothesis as
H0: μ1=μ2 against Ha: μ1 ≠ μ2
The level of significance is α=0.1
Since the population have unequal variances , the test statistic if H0 is true ,is
t`= x1`- x2`/ √s₁²/n1 + s₂²/n2
which has approximately a t- distribution with υ degrees of freedom where
υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
Computations:
t`= x1`- x2`/ √s₁²/n1 + s₂²/n2
t`= 46-31/ √4²/9 + 5²/12
t`= 15/√16/9 +25/12
t`= 15/ √64+75/36
t`=15/1.9649
t`=7.6339
t`= 7.63
υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
= [139/36]²/ (16/9)²/8 +(25/12)²/11
= 14.91/ 0.395 + 0.395
= 18.885
≈19 The degrees of freedom is always rounded in this calculation.
The critical region is ║t`║≥ t 0.05,19 = 1.729
Since the calculated value of t` falls in the critical region we reject our null hypothesis of equal means.
Which of the following is the correct answer after multiplying both sides of the inequality -x > -3 by -1?
x 3
x > -3
x < -3
Answer:
x < 3
Step-by-step explanation:
When you multipy an inequality by a negative, remember to switch the inequality sign!
-x > -3
(-x)(-1) > (-3)(-1)
x < 3
please give thanks and hit the heart button :)
Step-by-step explanation:
x<3
ph0t0math/máthwáy
y=3x-5
6x+3y=15
what is the value of y in the following system
y=3x - 5....(i)
6x+3y=15.....(ii)
Then,
Keeping value of y in (ii)equation;
or,6x+3(3x-5)=15
or,6x+9x-15=15
or,15x=15+15
or,x=30/15
:x=2
Now, Keeping value of x in (i) equation;
y= 3x-5
or, y= 3×2 - 5
or,y= 6-5
: y=1
ILL GIVE BRAINLEST HELP SOLVE THE GRAPH
How high is the peak of the Matterhorn? Below is a picture of the Matterhorn in Switzerland. As a surveyor, it is your job to estimate the elevation of the mountain. Using a device called a theodolite, you measure two angles from the horizontal plane to the top of the mountain as shown below. You also record the distance between the two measurements to be 1500 ft. Your elevation is known to be at 9,756ft above sea level. Determine the height of the Matterhorn (above sea level) to the nearest foot.
Answer:
[tex]E\approx14,962\text{ feet}[/tex]
Step-by-step explanation:
Please refer to the attachment below.
As shown, we can split the diagram into a scalene triangle and a right triangle.
The strategy here is to use the Law of Sines to find x, then use right triangle ratios to find h, the height of Matterhorn (with respect to our elevation).
Let’s start with the scalene triangle.
To use the Law of Sines, we will need two angles and the sides opposite to the angles.
Since we need to find x, we need the angle opposite to x. This is already given to us as 30°.
We can use the side that measures 1,500. The angle opposite to it θ is unknown.
So, we will need to determine θ. From supplementary angles, we know that:
[tex]\alpha+35=180[/tex]
So, it follows that:
[tex]\alpha=145^\circ[/tex]
The interior angles of a triangle always sum to 180°. Hence:
[tex]30+\alpha+\theta=180[/tex]
By substitution:
[tex]30+145+\theta=180[/tex]
Hence:
[tex]\theta=5^\circ[/tex]
Now, we can use the Law of Sines, given by:
[tex]\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}[/tex]
It is important to align the angles correctly with the sides.
So, we will substitute θ = 5° for A and 1,500 for a.
And we will substitute 30° for B and x for b. Hence:
[tex]\displaystyle \frac{\sin(5^\circ)}{1,500}=\frac{\sin(30^\circ)}{x}[/tex]
Solve for x. Cross-multiply:
[tex]x\sin(5^\circ)=1500\sin(30^\circ)[/tex]
Hence:
[tex]\displaystyle x=\frac{1500\sin(30^\circ)}{\sin(5^\circ)}[/tex]
When doing trigonometry (or any math, really), try not to round intermediate values, as this may result in inaccuracies in the final answer. Hence, we will leave this as is.
Now, we can use the right triangle.
We know that an angle is 35°.
The height h is opposite to our angle.
And x was our hypotenuse. Therefore, we can use the sine ratio given by:
[tex]\displaystyle \sin(x^\circ)=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
In this case, our angle is 35°.
The opposite side is h.
And the hypotenuse is x. Hence, by substitution:
[tex]\displaystyle \sin(35^\circ)=\frac{h}{x}[/tex]
Solve for h. Multiply both sides by x:
[tex]h=x\sin(35^\circ)[/tex]
Since we already know the value of x:
[tex]\displaystyle h=\frac{1500\sin(30^\circ)}{\sin(5^\circ)}\cdot\sin(35^\circ)[/tex]
Simplify. So, the height of Matterhorn with respect to our current elevation is:
[tex]\displaystyle h =\frac{1500\sin(30^\circ)\sin(35^\circ)}{\sin(5^\circ)}[/tex]
The total elevation of Matterhorn will be the current elevation of the surveyor plus the height with respect to the current elevation or simply h. So, the elevation height is:
[tex]E=9756+h[/tex]
By substitution:
[tex]\displaystyle E=9756+\frac{1500\sin(30^\circ)\sin(35^\circ)}{\sin(5^\circ)}[/tex]
Now we may approximate. Use a calculator. So, the total elevation of Matterhorn is:
[tex]E=14961.78867...\approx14,962\text{ feet}[/tex]
is y = 2x + 6 proportional or non-proportional?
The number of adult Americans from a random sample of n adults who support a bill proposing to extend daylight savings time is a binomial random variable. Assume that its probability will be approximated using the normal distribution. Describe the area under the normal curve that will be computed in order to determine the probability that more than 368 Americans support the bill.
Answer:
Right of X = 368.5
Step-by-step explanation:
By using the normal approximation to the Binomial random variable, we normally make use of continuity correction.
Using the rule of continuity;
P(X > K) turn out to be P(X > K + 0.5)
To determine the required probability:
∴
P(X > K) turn out to be P(X > K + 0.5)
P(X > 635) turn out to be P(X > 368 + 0.5)
⇒ P(X > 368.5) to the right.
Right of X = 368.5
How many tenths are there in 2.7?
Answer:
There are 7 tenths
Step-by-step explanation:
The tenths spot is the first spot over to the right of the decimal place, so there are 7 tenths
As we know that 10 tenths are there in 1 so, there are total 27 tenths are there in the 2.7
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
10 tenths make up one, hence there are,
2.7 × 10 = 27 tenths in 2.7
There is one more way to check this,
2.7 ÷ (1/10)
= 2.7 × 10
= 27
To know more about arithmetic operations:
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The cost of admission to the zoo is $10 for adults and $5 for children. How much will it cost for 7 adults and 12 children to go to the zoo
Answer:
it will cost 130
Step-by-step explanation:
10x7=70 12x5=60 60+70=130
Solve for x. Need help please
Answer:
3
Step-by-step explanation:
2x+6=5x-3
9=3x
x=3
Jaxon is deciding between two landscaping companies for his place of business. Company A charges $45 per hour and a $150 equipment fee. Company B charges $35 per hour and a $200 equipment fee. Let
A
A represent the amount Company A would charge for
t
t hours of landscaping, and let
B
B represent the amount Company B would charge for
t
t hours of landscaping. Write an equation for each situation, in terms of
t
,
t, and determine the interval of hours,
t
,
t, for which Company A is cheaper than Company B.
Answer
10 hours
Explanation
Step one:
given information
Company A
charges $45 per hour and a $150 equipment fee.
Let A represent the amount Company A would charge for t hours
So, the expression for the total is
A= 45t+150--------------------1
Company B
charges $35 per hour and a $200 equipment fee.
Let B represent the amount Company B would charge for t hours
So, the expression for the total is
B= 35t+200--------------------2
Step two:
equating the two equations above
A=B
45t+150=35t+200
collect like terms
45t-35t= 200-150
5t=50
divide both sides by 5
t=50/5
t=10
What is the limit of [(x+2) /(x+1)] ^x as x approaches to infinity?
first thing we need to do is factorise because we can't calculate infinity/infinity
and we are left with 1^infinity this is an euler function
an euler function looks like this
The waitress brings you your bill for $82.43 at a fancy restaurant. You want to leave a 20% tip for the waitress. How much money should you pay in order to cover the bill and the waitress's tip?
Answer:
98.91
Step-by-step explanation:
rounded to 2 decimal places
a. What is the decimal for 1 trillionth of a second?
Answer:
Step-by-step explanation:
1 000 000 000 000 E12
Answer:
Step-by-step explanation:
0.000 000 000 001
What expression is equivalent to 1/3 divided by 1/6 plz help me
Answer:
The answer is B. 1/3 * 6/1
Step-by-step explanation:
When dividing fractions, you multiply the first term in the expression by the reciprocal of the 2nd term.
please help me pls
Answer:
th answer is 10.
Step-by-step explanation:
in the pic. can i get brainlist
Answer:
64
Step-by-step explanation:
First, we multiply by 4 on both sides to get rid of the pesky fraction. We get:
x - 24 = 40
Now we add 24 on both sides to isolate the x and get all of the numbers on the other side:
x = 64
To check our work, we can input our answer back into the equation:
(64)/4 - 6 = 16 - 6 = 10
This satisfies the equation. Therefore, x = 64 is our answer!
I hope this helps! :)
In a 2^4 factorial design, the number of degrees of freedom for the model, assuming the complete factorial model, is:_____
a. 7
b. 5
c. 6
d. 11
e. 12
f. none of the above.
Answer:
None of the above
Step-by-step explanation:
Given
[tex]Design = 2^4[/tex]
Required
Determine the degree of freedom (df)
df is calculated as follows;
[tex]df = N- 1[/tex]
In this case:
N = Number of designs,
[tex]N = 2^4[/tex]
[tex]N = 16[/tex]
Substitute 16 for N in [tex]df = N- 1[/tex]
[tex]df = 16 -1[/tex]
[tex]df = 15[/tex]
Hence, none of the options answer te question
The grocery store sells orange juice in glass or plastic bottles. The glass bottles hold 5 liters of orange juice and the plastic bottles hold 1 liter of orange juice. Harper bought 46 liters of orange juice. The juice came in 14 bottles. How many of each type of bottle did she buy?
Please help me fast!!
Answer:
(8 glass bottles and 6 plastic bottles)
Step-by-step explanation:
(8 glass bottles = 40 liters) +(6 plastic bottles = 6 liter) = 46 liters of orange juice
8 bottles plus 6 bottles equals 14 bottles
all criteria is fulfilled.
I have 86 chocolate chip cookies and 42 sugar cookies what is the greatest number of identical packages that I can make
Assuming there can only be 2 cookies per identical package, She can make 42 identical packages which contains 2 chocolate chip cookies and 1 sugar cookie.
86 / 2 = 43 chocolate chips cookies
42 / 1 = 42 sugar cookies
With the sugar cookies not having the capability to match the requirements we will assume for this answer that an "Identical Package" is composed of 2 chocolate chip cookies, and a single sugar cookie.
PLEASE HELP FIND ANGLE Z
round each decimal to nearest whole number
23.18
pls help this is not graded
Answer:
3rd one
Step-by-step explanation:
100000+7e7e73t6r6r67r2w6r
Answer:
5.1
Step-by-step explanation:
hope this helps
Luis deposited $500 into his savings account with a simple interest rate of 3%. He wants to keep his deposit in the bank until he earns $120 in interest. For how many years does Luis need to keep his deposit in the bank?
Answer:
Blac cack
Step-by-step explanation:
For an acute angle θ, the equation sin(θ)=cos(6) is true. What is the value of θ? Show or explain your answer
Answer:
(θ) = 84°
Step-by-step explanation:
Given:
sin(θ)=cos(6)
Find:
value of θ
Computation:
sin(θ)=cos(6)
We know that
cos(90-a) = sin(a)
So,
sin(θ)=cos(90-84)
sin(θ)=sin(84)
So,
(θ) = 84°
The value of (θ) = 84°
Given that,
The equation is sin(θ)=cos(6)Based on the above information, the calculation is as follows:
sin(θ)=cos(6)
We know that
cos(90-a) = sin(a)
So,
sin(θ)=cos(90-84)
sin(θ)=sin(84)
So,
(θ) = 84°
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Many firms use on the job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performances of one of the trainees on the final test that was given to all trainees. The mean of the test score is 78. Additional information indicated that the median of the test scores was 85. What type of distribution most likely describes the shape of the test scores
Answer:
Skewed to the left
Step-by-step explanation:
In pearson mode skewdness, the mean, mode and median are used to determine if we have a positive or negative skewed distribution.
Now, If the mean is greater than the median, it means that the distribution is positively skewed and therefore skewed to the right. However, If the mean is less than the median, it means that the distribution is negatively skewed and therefore skewed to the left.
In our question, the median is 85 and mean is 78. Thus, it means median is greater than the mean and as such, the distribution isnegatively skewed and therefore skewed to the left.
Helppppppp:)!!!!!!!
:)))))))))
Answer:
-5a
Step-by-step explanation:
-21 + 16 = 16-21 16-21= -5 Therefore, a=-5
Give Brainliest if I helped Please!