Step-by-step explanation:
sinA/tanA
=>sinA ÷ sinA/cosA
=>sinA x cosA/sinA
=>cosA
Step-by-step explanation:
Hey there!
LHS
[tex] = \frac{ \sin(a) }{ \tan(a) } [/tex]
[tex] = \sin(a) \times \frac{ \cos(a) }{ \sin(a) } [/tex]
= cos A
Proved!!
Hope it helps!
In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 23 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x=8.16 cm3 and s=0.7 cm3. Conduct the appropriate test at the α=0.01 level of significance.
Answer:
We do not reject the Null Hypothesis
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=23[/tex]
Population mean [tex]\mu=9.02cm^3[/tex]
Sample mean [tex]\=x=8.16[/tex]
Standard deviation [tex]\sigma=0.7cm^3[/tex]
Significance level [tex]\alpha =0.01[/tex]
Generally the Null and and alternative Hypothesis are as follows
[tex]H_0:\mu=9.02cm^3[/tex]
[tex]H_a:\mu<9.02cm^3[/tex]
Therefore t critical Value is
[tex]t\ critical\ Value=(\alpha,df)[/tex]
[tex]t\ critical\ Value=(0.01,22)[/tex]
Where
[tex]df=n-1\\\\df=23-1=>22[/tex]
Therefore
From t Table
[tex]t value=-2.8[/tex]
Generally the equation for Z Critical is mathematically given by
[tex]t=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]t=\frac{8.16-9.02}{\frac{0.7}{\sqrt{23} } }[/tex]
[tex]t=-5.89[/tex]
Therefore
Since the t test statistics is greater than the Critical value
Hence,we do not reject the Null Hypothesis
Find the volume of the frog queen building in Graz, Austria. The building is 18 meters long, 17 meters tall, and 18 meters wide
Answer: 5,508 m3
Step-by-step explanation: V= 18 x 17 x 18 = 5,508 m3
Answer:5, 508
Step-by-step explanation:
V 18×18×17=5,508
Somebody help please.
Answer:A
Step-by-step explanation: The formula for finding volume is LxWxH. 21x 11 is 231, and since one side is 11 so will the other side be, and then you get 2,541 m cubed.
Use algebra to solve 3x+4 = 1/x
The exact solutions are x=
Х
Answer:
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{2±\sqrt{7} }{3}[/tex]
Step-by-step explanation:
3x + 4 = 1 ÷ x
3x + 4 - 4 = 1 ÷ x - 4
3x = 1 ÷ x - 4
[tex]3x=\frac{1}{x} +\frac{x(-4)}{x}[/tex]
[tex]3x=\frac{1+x(-4)}{x}[/tex]
[tex]3x=\frac{1-4x}{x}[/tex]
[tex]x(3x)=x(\frac{1-4x}{x})[/tex]
x · 3x = - 4x + 1
3x² = - 4x + 1
3x² - (- 4x + 1) = 0
3x² + 4x - 1 = 0
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 3
b = 4
c = - 1
[tex]x=\frac{-4±\sqrt{4^{2}-4((3)(-1)) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{16-4((3)(-1)) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{16+12 } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{28 } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{(2)(14) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{(2)(2)(7) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{2 } \sqrt{2}\sqrt{7} }{2(3)}[/tex]
[tex]x=\frac{-4±2\sqrt{7} }{2(3)}[/tex]
[tex]x=\frac{-4±2\sqrt{7} }{6}[/tex]
Two separate equations
[tex]x=\frac{-4+2\sqrt{7} }{6}[/tex]
[tex]x=\frac{2+\sqrt{7} }{3}[/tex]
[tex]x=\frac{-4-2\sqrt{7} }{6}[/tex]
[tex]x=\frac{2-\sqrt{7} }{3}[/tex]
A certain radioactive isotope is a by-product of some nuclear reactors. Due to an explosion, a nuclear reactor experiences a massive leak of this radioactive isotope. Fortunately, the isotope has a very short half-life of 13 days. Estimate the percentage of the original amount of the isotope released by the explosion that remains 6 days after the explosion.
Answer:
[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]
Step-by-step explanation:
The following formula can be utilized for this question:
[tex]N = N_o (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\\frac{N}{N_o} = (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\[/tex]
where,
[tex]\frac{N}{N_o}[/tex] = ratio of the remaining amount to the original amount = ?
t = tme passed = 6 days
[tex]t_{1/2}[/tex] = half-life = 13 days
Therefore,
[tex]\frac{N}{N_o} = (\frac{1}{2} )^{\frac{6\ days}{13\ days} }\\\\[/tex]
[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]
A department store, on average, has daily sales of $21,000. The standard deviation of sales is $3600. On Tuesday, the store sold $16,230 worth of goods. Find Tuesday's z score. What is the percentile rank of sales for this day
Answer:
Tuesday's z-score was of -1.325.
The percentile rank of sales for this day was the 9.25th percentile.
Step-by-step explanation:
Z-score:
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.
A department store, on average, has daily sales of $21,000. The standard deviation of sales is $3600.
This means that [tex]\mu = 21000, \sigma = 3600[/tex]
On Tuesday, the store sold $16,230 worth of goods. Find Tuesday's z score.
This is Z when X = 16230. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16230 - 21000}{3600}[/tex]
[tex]Z = -1.325[/tex]
Tuesday's z-score was of -1.325.
What is the percentile rank of sales for this day
This is the p-value of Z = -1.325.
Looking at the z-table, this is of 0.0925, and thus:
The percentile rank of sales for this day was the 9.25th percentile.
Marcus likes to go for a run each morning before school. He recorded the number of minutes he spends running and the distance he covers. The scatter plot represents the data he collected
Answer:
D. 0.85
Step-by-step explanation:
The data points in the scatter plot are closer to each other along the line of best fit, this means that there is a strong positive association between minutes and distance and therefore, the correlation coefficient would be relatively closer to 1.
The correlation is positive since both variables tend to increase together in the same direction.
Therefore, the best estimate of the correlation coefficient out of the given options would be 0.85
Teresa is making iced tea. She has a container that has a volume of 3.95 gallons to store the iced tea.
Find the net change in the value of the function between the given inputs.
h(t) = t2 + 9; from −4 to 7
Determine the equation of the circle shown in the graph.
Answer:
B.
Step-by-step explanation:
The equation of a circle with center at (h, k) and radius r is
[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]
We have center at (-5, 0). That makes h = -5, and k = 0.
The radius is 3, so r = 3.
[tex] (x - (-5))^2 + (y - 0)^2 = 3^2 [/tex]
[tex] (x + 5)^2 + y^2 = 9 [/tex]
Answer: B.
Answer:
B
Step-by-step explanation:
The equation of a circle has the form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the center of the circle and r is the radius.
From the graph, we can see that the center of the circle is at (-5, 0). So, (h, k) is (-5, 0), where h = -5 and k = 0.
And by counting, we can determine that the radius of the circle is three units. Hence, r = 3.
Substitute the information into the equation:
[tex](x-(-5))^2+(y-(0))^2=(3)^2[/tex]
Simplify. Therefore, our equation is:
[tex](x+5)^2+y^2=9[/tex]
Our answer is B.
What is the volume of a cone that has a radius of 11.2 cm and a height of 25.3 cm?
Your Answer:
Sim
Step-by-step explanation:
V≈3323.42cm³
r Radius
11.2
cm
h Height
25.3
cm
Solution
V=πr2h
3=π·11.22·25.3
3≈3323.41966cm³
hope it is helpful
Nikki bought a patio set on sale for $480. The original price was $850. What was the rate of discount?
Round your answer to the the nearest tenth of a percent
Answer:
43.5 % decrease
Step-by-step explanation:
Take the original price and subtract the new price
850-480
370
Divide by the original price
370/850
.435294118
Change to percent form by multiplying by 100
43.5294118 % decrease
43.5 % decrease
PLEASE HELPP!!!!
Find the probability that a randomly selected point within the circle falls in the white area. r= 4 cm 2.5 cm 3 cm 3 cm [? ]% Round to the nearest tenth of a percent.
Answer:
61.2%
Step-by-step explanation:
because i just did it and got it right
The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When
the length is 12 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm/s)? Write an equation for A in terms of l and w.
Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
[tex]A=w\ell[/tex]
Where w is the width and l is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to t, where w and l are both functions of t:
[tex]\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell][/tex]
By the Product Rule:
[tex]\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w[/tex]
Since we know that dl/dt = 6 and that dw/dt = 5:
[tex]\displaystyle \frac{dA}{dt}=5\ell + 6w[/tex]
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
[tex]\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}[/tex]
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
what is the evaluation 7w -14 for w = 9
Answer:
7w - 14
if w = 9
7(9) - 9
63 - 9
w=57
What does the digit 8 represent in 687,413?
Eight hundred thousand
Eight thousand
Eight hundred
O Eighty thousand
Answer:
Eighty thousand
Step-by-step explanation:
Look at the place value chart.
PLEASE HELP ME WILL MARK YPU IF YOU HELP ME
ok check image file in the image is answers with color code
What's the answer to this? and please explain.
===========================================================
Use this formula
a & b/c = (a*c+b)/c
to convert from a mixed number to an improper fraction
So,
a & b/c = (a*c+b)/c
3 & 3/4 = (3*4+3)/4
3 & 3/4 = 15/4
---------------------------------------------------
Next, we add the fractions 15/4 and 5/6. The denominators aren't the same, so we can't add right away. We need to get the denominators to the LCD.
In this case, the LCD is 4*6 = 24
The fraction 15/4 becomes 90/24 after multiplying top and bottom by 6.The fraction 5/6 becomes 20/24 after multiplying top and bottom by 4Now we can add the fractions:
90/24+20/24 = (90+20)/24 = 110/24
---------------------------------------------------
So far, we've added the 3&3/4 portion to the 5/6 portion to get the result 110/24
The last thing to do is to add on the two 1/3 ft pieces, which means we're adding on 2/3 of a foot
2/3 = 16/24 after multiplying top and bottom by 8
Add this to the result of the last section
110/24+16/24 = (110+16)/24 = 126/24
---------------------------------------------------
From here, we convert the improper fraction 126/24 to decimal form
Using a calculator, you should find that 126/24 = 5.25
The result is larger than 5, which means she used too much ribbon. There won't be enough ribbon to do everything she wants to do.
---------------------------------------------------
The shortcut we can take is to type the following into the calculator
3+3/4+5/6+2/3
doing so should lead to 5.25
Answer:
Yes
Step-by-step explanation:
So at the begining, Cherly has 60 in (12inx5ft) of ribbon. She uses 45 in(3.75x12) to make the hair bow, leaving 15 in of ribbon. She, then, uses 10 in (5/6x12) of ribbon, leaving 5 in. After that, Cheryl uses 8 in [2(1/3x12)] to put on the picture frame, leaving two inches of ribbon.
A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Interest amount paid on loan = $90
Principal value, amount borrowed = $500
Period, t = 16 days
The equivalent annual interest :
Using the simple interest formula :
simple interest = principal * rate * time
Using, days of year = 365
Plugging in the values into the formula :
90 = 500 * rate * (16/365)
90 = 500 * rate * 0.0438356
90 = 21.917808 * rate
Rate = 90 / 21.917808
Rate = 4.10 = 4.10 * 100% = 410%
If days of year = 360 is used :
90 = 500 * rate * (16/360)
Rate = 90 / 22.222
Rate = 4.05 = 4.105 * 100% = 405%
To complete a task in 30 days a company needs
4 people each working for 7 hours per day.
The company decides to have
5 people each working for 6 hours per day.
Assuming that each person works at the same rate,
how many days will the task take to complete?
Answer:
28 days
Step-by-step explanation:
4 x 7 x 30= 840 total working hours
5 x 6 x n = 840
= n = 840 ÷ 30
= n = 28 days
The task will take approximately 1 day to complete with 5 people working for 6 hours per day.
Determining the time to complete the taskTotal work done in the first scenario = 4 × 7 × 30
= 840 work hours
Total work done in the second scenario = (5 × 6 × D)
= 4 × 7 × 30
Solving for D:
30D = (4 × 7 × 30) / (5 × 6)
D = (4 × 7) / (5 × 6)
D = 28 / 30
D ≈ 0.9333
Rounding up to the nearest whole day, D = 1
Therefore, the task will take approximately 1 day to complete with 5 people working for 6 hours per day.
Learn more on time calculation here https://brainly.com/question/26046491
What is 2 3 of 99kg?
Step-by-step explanation:
[tex] \frac{2}{3} \times \frac{99}{1} = 66 \: kg[/tex]
There are 13 apples in a basket. 4 of these apples are green. The rest are red. what is the ratio?
Answer:
9:4 4:13
Step-by-step explanation:
Answer:
a) 9:4 b) 13 : 9
Step-by-step explanation:
13 = total
4 = green
13-4 ( which Is 9) = red
Ratio of red apples to green apples?
9:4
RATIO of all apples to red
13: 9
WILL GIVE BRAINLIESTTT!!!! PLS HELP
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Create a proportion using the form %/100 = is/of to represent the following word problem.
Seven is what percent of 30?
The ordered pairs in the table below represent a linear function.
Answer:
2
Step-by-step explanation:
ordered pairs are
(2 , 3) = (x1 , y1)
(5 , 9) = (x2 , y2)
slope = y2 - y2 / x2 - x1
= 9 - 3 / 5 - 2
= 6 / 3
= 2
Plsssss help I’ll put you as a brainiest answer
Answer:
your answer would probably be 20 bc I times 5 then times 2 then I got 10. Then I did 10 X 2 and I got 20
VIVIAN: My friend Sharon told me today that she will be driving back to Victorville, her hometown, this weekend for the first time in almost two years. NATALIE: You must not have been listening very carefully to what Sharon was saying, because I know for sure that Sharon's hometown is Vacaville, not Victorville.
Is dispute C a verbal dispute or a factual dispute?
a. Factual
b. Verbal
Answer:
The answer is "Option a".
Step-by-step explanation:
Dispute C comes under factual dispute because the words Vacaville or Victorville are two different places and they are arguing about the fact that's why option a is correct.
Which equation can be simplified to find the inverse of y = 2x2
Answer: d
Step-by-step explanation:
edge 2020
PLS HELP! I NEED TO FIND THE SURFACE AREA OF THIS CYLINDER!
PLS PROVIDE A STEP BY STEP EXPLANATION! ❤️
5 x 10 - 2 = ??
HALP MOIIIIIIIIIIIIIIIIIIIIII
Answer:
48
Step-by-step explanation:
the answer is 48 I got this answer by multiplying 5 by 10 and subtracting is from 2 which gives me 50 - 2 which is 48
Answer:
48
Step-by-step explanation:
5×10-2=50-2
=48
hope it helps!!
The bike you have been saving for is discounted 25%. You have $500 saved to purchase it. The original, non-discounted price of the bike is $575. There is a 5.60% sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax, how much money will you have left over? Round your answer to the nearest dollar.
