Answer:
Cosine W = 0.32
Step-by-step explanation:
Adj/Hypo = 12/37 = 0.3243 = 0.32
Final answer:
The cosine of ∠W in triangle ΔVWX is found by dividing the length of the side adjacent to ∠W (XW) by the length of the hypotenuse (WV), resulting in cos(∠W) ≈ 0.32 to the nearest hundredth.
Explanation:
In triangle ΔVWX, where ∠X=90°, VX = 35, XW = 12, and WV = 37, we are asked to find the value of the cosine of ∠W to the nearest hundredth. Since ∠X is a right angle, this triangle is a right triangle, and we can use trigonometric ratios to find the cosine of ∠W. The cosine of an angle in a right triangle is equal to the adjacent side over the hypotenuse.
To find the cosine of ∠W, we look at the sides adjacent to ∠W, which are XW and WV. The length of XW is 12, and WV, being the hypotenuse, is 37. Therefore, to find cos(∠W), we calculate 12/37. Doing this calculation, we get cos(∠W) ≈ 0.32 to the nearest hundredth.
The cosine is a trigonometric function that relates the lengths of sides in a right triangle to the angles, and it is specifically the ratio of the length of the adjacent side to the length of the hypotenuse.
Marta and Kim are sisters. Five years ago Kim's age was twice as great as martas age. If Marta is no m years old, what expression represents Kim's age now?
Answer:
y = 2m-5
Kim's age now is y = 2m-5
Step-by-step explanation:
Let m represent martas age now and y represent Kim's age now
Given;
Five years ago Kim's age was twice as great as martas age.
(y-5) = 2(m-5)
Solving for y;
y-5 = 2m-10
y = 2m-10+5
y = 2m-5
Kim's age now is y = 2m-5
Final answer:
Kim's current age is represented by the expression 2m - 5, where m is Marta's current age. This is determined by considering the age difference and relationship of their ages five years ago.
Explanation:
The question is about determining Kim's current age given that Marta is currently m years old and five years ago Kim's age was twice that of Marta's. To solve this, we can follow these steps:
Let's represent Marta's age five years ago as m - 5.
Since Kim's age was twice Marta's age five years ago, we express Kim's age at that time as 2(m - 5).
To find Kim's current age, we add five years to her age at that time: 2(m - 5) + 5.
Simplifying the expression gives us Kim's current age as 2m - 5.
Therefore, the expression that represents Kim's age now, given that Marta is m years old, is 2m - 5.
We have 2 stacks or styrofoam cups one has 6cups and it's height is 15cm.The other stack has 12cups and Height is 23cm. How many cups are needed for a stack with the height of 50cm?
Answer:
Given
Number of stacks = 2
Stack 1 = 6 cups; h1 = 15cm
Stack 2 = 12 cups; h2 = 23cm
Let's first find the average:
[tex] \frac{H_1 - H_2}{ n_1 - n_2}[/tex]
[tex]= \frac{15-23}{6-12} [/tex]
[tex] = \frac{-8}{-6} = \frac{4}{3} [/tex]
With an average of 4/3, to obtain the number of cups needed to obtain a height of 50m, we have:
50 / (4/3)
= 50 * 3/4
= 150/4
= 37.5
From the answer, we can see that the number of cups is not really proportional to the height of the stack, because the average of stack one and stack 2 are different.
The number of pupils in school A is equal to half the number of pupils in school B. The ratio of the boys in school A and the boys in school B is 1:3 and the ratio of the girls in school A and the girls in school B is 3:5. The number of boys in school B is 200 higher than the number of boys in school A. Find the number of boys and girls in each school.
Answer:
There are 100 boys and 300 girls in School A and there are 300 boys and 500 girls in School B .
Step-by-step explanation:
The ratio of the boys in school A and the boys in school B is 1:3
Let the ratio be x
No. of boys in School A = x
No. of boys in School B = 3x
We are given that The number of boys in school B is 200 higher than the number of boys in school A.
So,[tex]x+200=3x[/tex]
[tex]200=3x-x[/tex]
[tex]200=2x[/tex]
[tex]\frac{200}{2}=x[/tex]
100=x
So, No. of boys in School A = x = 100
No. of boys in School B = 3x =3(100)=300
We are given that the ratio of the girls in school A and the girls in school B is 3:5.
Let the ratio be y
So, No. of girls in School A = 3y
No. of girls in School B = 5y
So, Total No. of students in School A= No. of boys in school A + No. of girls in school A=100+3y
Total No. of students in School B= No. of boys in school B + No. of girls in school B=300+5y
We are given that The number of pupils in school A is equal to half the number of pupils in school B.
So, [tex]100+3y=\frac{1}{2}(300+5y)[/tex]
[tex]200+6y=300+5y[/tex]
[tex]y=100[/tex]
No. of girls in School A = 3y=3(100)=300
No. of girls in School B = 5y=5(100)=500
Hence there are 100 boys and 300 girls in School A and there are 300 boys and 500 girls in School B .
Answer: 100 boys, 300 girls in School A. 300 boys,500 girls in School B
Step-by-step explanation:
A triangle has sides of 15 and 27. The measurement of the longest side is missing.
Ted says that one possibility for the unknown side length is 40. Do you agree with Ted? Why or why not?
Answer:
Step-by-step explanation:No if you use soh cah toa
The fraction
17
100
can be written as which decimal?
Answer:
.17
Step-by-step explanation:divide 17 by 100 hope this helps god bless
Answer:
0.17
Step-by-step explanation:
Really need to know this for math!
Which number represents 10. Helpful if you answer all the rest ASAP
Answer:
I had to look up the problem B4 because your image doesn't show the rest of the information
B4 = 12
B5 = 1,738
Step-by-step explanation:
if you need help on any other questions on this, i can't see them in the image
Which one is bigger 4.5 kg or 4.050
Answer:
4.5 kg
Step-by-step explanation: if you have 4.050 take off the zero and it is only 4.05 which is less then 4.5 or 4.50
Final answer:
When comparing 4.5 kg to 4.050 kg, 4.5 kg is the larger weight since both are in kilograms and 4.5 is greater than 4.050.
Explanation:
The question asks which number is larger, 4.5 kg or 4.050 kg. In the metric system, weights are compared directly as they are expressed in the same units. Here, we compare 4.5 to 4.050. Since 4.5 can also be thought of as 4.500 when considering the decimal places, it becomes clear that 4.5 kg is the larger value because both represent kilograms, and 4.5 is greater than 4.050.
Use properties of rational number to simplify the expression.
A.)129/7
B.)262/15
C.)122/7
D.)507/28
Answer:
A.)129/7
Step-by-step explanation:
25/4 + 24/7 + 35/4
I will add the two with common denominator together first
25/4 + 35/4 +24/7
60/4 +24/7
15 + 24/7
We need to get a common denominator of 7
15 *7/7 + 24/7
105/7 + 24/7
129/7
what does x equal in this equation x−9.37+5.77=1.3x
Answer:
-12
Step-by-step explanation:
x-9.37+5.77=1.3x
Charlie has 7 cards, numbered 2, 3, 4, 5, 6, 7, 8, 9. What is the probability of picking an odd card? Give your answer as a fraction, a decimal, and a percent. Round to the nearest hundredth.
There are 4 out of the 7 cards that are odd numbers.
As a fraction: 4/7
As a percent: 57.14%
As a decimal: 0.57
Is 3√124 the same as 6√31?
Answer:
Yes
Step-by-step explanation:
[tex]3\sqrt{124} = 3\sqrt{4} \sqrt{31} \\\sqrt{4} = 2\\ 3*2\sqrt{31}=6\sqrt{31}[/tex]
A box of cereal has a volume of 336 cubic inches. If the width of the box is 4 inches and the length is 7 inches, what is the height of the box
I'm confused
Answer:
12 inches
Step-by-step explanation:
Volume = length × width × height
336 = 4 × 7 × height
height = 12
Answer:
12 cubic inches.
Step-by-step explanation:
Since volume is length x width x height, you just do 7 x 4 (28) and then the total, 336 and divide that by 28. So, 12 cubic inches!
find an angle in the normal range (0 degrees to 360 degrees, or 0 to 2pi radians) whose terminal side points in the same direction as the terminal side of an angle measuring -11pi/3.
Answer:
a) pi/3
Step-by-step explanation:
-11pi/3 + 4pi
(-11+12)pi/3
pi/3
Answer:
A
Step-by-step explanation:
We see that the angle is -11[tex]\pi[/tex]/3, which means that when drawing this angle on the graph, we need to move clockwise from 0 (see the drawing).
We see that this angle is actually the exact same as an angle in the first quadrant. This angle is [tex]\pi[/tex]/3.
Thus, the answer is A.
Hope this helps!
3. The annual per capita consumption of fresh bananas in the United States can be approximated by a normal distribution, with a mean of 10.4 pounds and a standard deviation of 3 pounds. What is the largest annual per capita consumption of bananas that can be in the bottom 5 % of consumption
Answer:
The largest annual per capita consumption of bananas in the bottom 5% of consumption is 5.465 lb
Step-by-step explanation:
Given
μ = Mean = 10.4 lb
σ = Standard deviation = 3 lb
Using a confidence level of 90%,
We'll need to first determine the z value that correspond with bottom 5% of consumption of banana
α = 5%
α = 0.05
So,
zα = z(0.05)
z(0.05) = -1.645 ----- From z table
Let x represent the largest annual per capita consumption of bananas
The relationship between x and z is
x = μ + zσ
By substitution;
x = 10.4 + (-1.645) * 3
x = 10.4 - 4.935
x = 5.465
Hence, the largest annual per capita consumption of bananas in the bottom 5% of consumption is 5.465 lb
To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 52 numbers (1 through 52). The order in which the selections is made does not matter. How many different 6-number selections are possible?
Answer:
The answer is 20,358,520
Step-by-step explanation:
Selecting 6 numbers from a collection of 52 numbers regardless of order involves a combination.
Note: if regards was taken into order of selection, this would be a permutation.
Hence, the different 6 number selections out of 52 is
52C6 = 52! / [6!*(52-6)!]
= 52!/(6!*46!)
= 20,358,520
Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 240 students and recorded how long it took each of them to find a parking spot. Identify the population of interest to the university administration.
Answer:
In this particular case,the target population of interest to the university administration constitutes the university students.Step-by-step explanation:
The university administration is interested to conduct a statistical study to identify the average or mean time taken by the students to find a vacant parking spot.Therefore,the research topic here is the average time taken by the university students to find parking spot. The administrator collects an inconspicuous sample of 240 samples from the target population of the study,which is the overall student population of the university.The sample collected by the university administration is used to observe the average or mean parking time by the university students.x² +10x+3=0
how do I slove it with the quadratic formula?
Answer:
Step-by-step explanation:
The equation is already in standard form [ ax² + bx + c = y ] so we can find the values of each variable.
a = 1
b = 10
c = 3
y = 0
Quadratic formula: [tex]x = \frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Solve using the formula:
[tex]x=\frac{-10+-\sqrt{10^2-4(1)(3)} }{2(1)}[/tex]
[tex]x=\frac{-10+-\sqrt{100 - 12} }{2}[/tex]
[tex]x=\frac{-10+-\sqrt{88} }{2}[/tex]
[tex]x=-5+-\sqrt{22}[/tex]
Therefore, the answer is [ x = -5 ± √22 ]
Best of Luck!
If the probability that it will rain tomorrow is 15, what is the probability that it will not rain tomorrow?
A .45
B .35
C .25
D .210
The volume of a cone of radius r and height h is given by V=πr²h³. If the radius and the height both increase at a constant rate of 12 cms/sec, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?
Answer:
The volume of cone is increasing at a rate 1808.64 cubic cm per second.
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}[/tex]
Volume of cone =
[tex]V = \dfrac{1}{3}\pi r^2 h[/tex]
where r is the radius and h is the height of the cone.
Instant height = 9 cm
Instant radius = 6 cm
Rate of change of volume =
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})[/tex]
Putting values, we get,
[tex]\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}[/tex]
Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.
Final answer:
The volume of a cone can be found using the formula V = πr²h³. To find the rate at which the volume is increasing, we differentiate the volume formula with respect to time and substitute the given values into the derivative formula. The volume is increasing at a rate of 15552π cubic centimeters per second.
Explanation:
To find the rate at which the volume is increasing, we need to differentiate the volume formula with respect to time.
Let's differentiate the volume formula V = πr²h³ with respect to time t:
dV/dt = π(2rh³(dr/dt) + r²h²(dh/dt))
Given that dr/dt = dh/dt = 12 cm/sec, r = 6 cm, and h = 9 cm, we substitute these values into the derivative formula:
dV/dt = π(2(6)(9³)(12) + (6²)(9²)(12))
dV/dt = π(11664 + 3888)
dV/dt = 15552π
Therefore, the volume is increasing at a rate of 15552π cubic centimeters per second.
What is the answer to this? I need help :(.
Answer:
Not proportional
Step-by-step explanation:
Hope it helps you in your learning process.
[tex] \frac{6}{6}=1\\\\
\frac{8}{24}= \frac{1}{3}\\\\
\frac{10}{50}= \frac{1}{5}\\\\
\frac{12}{84}= \frac{1}{7}\\\\
\therefore \frac{6}{6}\neq \frac{8}{24}\neq \frac{10}{50}\neq \frac{12}{84}[/tex]
Hence, given ratios are not proportional.
For a research project on rodents, 60 groundhogs were tagged and released. Later, researchers
counted 700 groundhogs, 12 of which had tags. To the nearest whole number, what is the best
estimate for the groundhog population?
The estimated size of the lemur population can be calculated using the mark and recapture technique.
Explanation:The estimated size of the lemur population can be calculated using the mark and recapture technique. The formula to estimate population size is:
N = (M * C) / R
where N is the estimated population size, M is the number of marked individuals in the second capture, C is the total number of individuals in the second capture, and R is the number of marked individuals recaptured in the second capture.
In this case, the number of marked individuals in the second capture is 11, the total number of individuals in the second capture is 49, and the number of marked individuals recaptured is 11. Plugging these values into the formula:
N = (11 * 49) / 11 = 49
Rounding to the nearest whole number, the estimated size of the lemur population is 49.
Learn more about estimating population size using mark and recapture here:
https://brainly.com/question/32370260
#SPJ11
Which animal shelter has the dog that weighs the least?
A)- shelter A
B)- shelter B
C)- Both shelters have a dog with the lowest weight of 8 pounds.
D)- Both shelters have a dog with the lowest weight of 10 pounds.
WILL GIVE BRAINLIEST ANSWER IF YOU ANSWER RIGHT!!!
Answer:
A_A_A_A_A_A_A_A_A_A_A_A_A_A_Step-by-step explanation:
on the box chart it shows that shelter A has the lightest dog
hope i helped :D
Answer:
shelter A. shelter B. Both shelters have a dog with the lowest weight of 8 pounds.
Step-by-step explanation:
Hope this helps :)
(3x+5) is a factor of the polynomial (a-1)x^3 + (a+1)x^2 - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorize the given expression completely.
Answer:
(3x + 5)(x + √3)(x - √3)
Answer:
a = 4
Step-by-step explanation:
(3x+5) is a factor of the polynomial (a-1)x³ + (a+1)x² - (2a + 1)x - 15
Means x = -5/3 is a root
(a-1)(-5/3)³ + (a+1)(-5/3)² - (2a + 1)(-5/3) - 15 = 0
-125a/27 + 125/27 + 25a/9 + 25/9 + 10a/3 + 5/3 - 15 = 0
a(-125/27 + 25/9 + 10/3) = 15 - 5/3 - 25/9 - 125/27
a(40/27) = 160/27
a = 4
Use the formula to find the lateral area and surface area of prism
Answer:
The answer to your question is 2046 in²
Step-by-step explanation:
Data
length = 30 in
base = 24 in
hypotenuse = 25 in
Process
1.- Calculate the height of the triangle using the Pythagorean theorem
c² = a² + b²
-Solve for b
b² = c² - a²
-Substitution
b² = 25² - 24²
-Simplification
b² = 625 - 576
-Result
b² = 49
b = 7 in
2.- Calculate the area of the base
Area = base x height
Area = 24 x 7 x 2
= 336 in²
3.- Calculate the lateral area
Area = 30 x 25 x2
= 1500 in²
4.- Calculate the last area
Area = 30 x 7
= 210
5.- Final area
Total area = 210 + 1500 + 336
= 2046 in²
hellplppppppp800x40÷80=
Answer:
400
Step-by-step explanation:
Answer:
800*400/80=400
Step-by-step explanation:
To work this out you would first start with 40/80. This is because when using BODMAS / BIDMAS you would start with whatever operation that comes first out of all the operations in the question. This gives you 0.5. Then you would multiply 0.5 by 800, this gives you 400.
1) Find what operation you should do first.
B- Brackets
O -Orders
D-Division
M-Multiplication
A-Addition
S-Subtraction
2) Divide 40 by 80.
[tex]40/80=0.5[/tex]
3) Multiply 0.5 by 800.
[tex]0.5*800=400[/tex]
Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of 3 ml. A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are:299.4 297.7 301.0 298.9 300.2 297.0Is this convincing evidence that the mean contents of cola bottles is less than the advertised300 ml? Test at the 5% significance level.
Answer:
No because there is sufficient statistical evidence to suggest that the mean contents of cola bottles is equal to 300 ml as advertised
Step-by-step explanation:
Here we have the measured contents as
299.4
297.7
301.0
298.9
300.2
297.0
Total = 1794.2
∴ Mean = 299.03
Standard deviation = 1.5
We have
[tex]z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]
Where:
[tex]\bar x[/tex] = Mean of sample = 299.03 ml
μ = Mean of population = 300 ml
σ = Standard deviation of population = 3 ml
n = Sample size = 6
α = 5% = 0.05
We set our null hypothesis as H₀ = 300 ml
Our alternative hypothesis is then Hₐ < 300 ml
Therefore, z = -0.792
The probability from z table is P = 0.2142
Since the P value, 0.2142 is > than the 5% significance level, 0.05 we accept the null hypothesis that the mean contents of cola bottles is 300 ml.
what the volume is of this solid
Answer:
336.
Step-by-step explanation:
8 x 7 x 6 = 336.
Feel free to let me know if you need more help! :)
Which lists the steps in the correct order to find the median of this data set?
24, 16, 23, 30, 18, 29
Answer:
23.5
Step-by-step explanation:
you put it in order and find the middle in this case is 23 and 24 then you add them and divide by two and get 23.5
Brianna has 6 bags of soil. Filling one flowerpot requires
1
3
of a bag of soil. How many flowerpots can be filled with these 6 bags?
Answer:
18
Step-by-step explanation:
6*3=18
Answer: 18
Step-by-step explanation: It's easy, you have to divide in order to get 18.
What is the surface area of the triangular pyramid shown? Round to the nearest tenth.
5.2
[Not drawn to scale]
A. 57.6
B. 69.6
C. 73.2
D. 87.6
Answer:
A. 57.6
Step-by-step explanation:
6 times 5.2 is 31.2. 4 times 5 is 20. 6 times 5 is 30. 6 times 5 is 30. (31.2/2)+(20/2)+30= 55.6 Then you round nearest tenth. 57.6.
Answer:
Aa 57.6
Step-by-step explanation:
It is correct
correct on E D G E N U I T Y