Answer:
x=2
y=√2
Step-by-step explanation:
You can tell from the angles that this is a 45, 45, 90 triangle. That would mean that the side given is x. Then the side "x" is x√2, and "y" is the same as x. So, that would mean the sides would be √2, √2, and 2.
Multiples of 6 and 14
Answer:
Step-by-step explanation:
6: 6, 12, 18, 24, 30, 36, 42, 48, 54
14: 14, 28, 42, 56
the LCM (least common multiple) is 42.
In a hatch chemical process, two catalysts arc being compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1 and a sample of 10 batches was obtained using catalyst 2. The 12 batches for which catalyst 1 was used gave an average yield of 85 with a sample standard deviation of 4, and the second sample gave an average of 81 and a sample standard deviation of 5. Find a 90% confidence interval for the difference between the population means, assuming that the populations are approximately normally distributed with equal variances
Answer:
The 90% confidence interval, C.I = (0.693, 0.7307)
Step-by-step explanation:
Catalysts 1 and catalyst 2 have the following statistical data;
Catalyst 1
The number of batches in the sample, n₁ = 12
The average yield by the 12 batches of catalyst 1, [tex]\overline x_1[/tex] = 85
The sample standard deviation, s₁ = 4
Catalyst 2
The number of batches in the sample, n₂ = 10
The average yield, [tex]\overline x_2[/tex] = 81
The standard deviation, s₂ = 5
F-test = s₂²/s₁² = 5²/4² = 1.5625
The degrees of freedom, df = n₁ + n₂ - 2
∴ df = 12 + 10 - 2 = 20
The critical-t at 90% confidence level = 1.725
The F-test < The critical-t, we pool the variance
The 90% confidence interval with the assumption of equal variance is given as follows;
[tex]The \ 90\% \ confidence \ interval= \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2} \times (s_p) \times \sqrt{\dfrac{1^{2}}{n_{1}}+\dfrac{1^{2}}{n_{2}}}[/tex]
[tex]s_p =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]
Therefore;
[tex]s_p[/tex] = √((12 - 1)×4² + (10 - 1)×5²)/(12 + 10 - 2)) ≈ 4.48
Therefore, we get;
[tex]C.I. = \left (85- 81 \right )\pm 1.725 \times 4.48 \times \sqrt{\dfrac{1}{12}+\dfrac{1}{10}}[/tex]
The 90% confidence interval, C.I = 0.693 < μ₁ - μ₂ < 7.307 = (0.693, 0.7307).
A survey was conducted at a town hall meeting to determine if a new park should be built. Out of the 3,462 people surveyed, 1,468 people voted that the town should not build a new park.
Assuming the survey was random, what percentage of people in the town would likely vote in favor of the new park?
Enter your answer to the nearest percent in the box.
%
Answer: 58%
Step-by-step explanation:
Answer:
58%
Step-by-step explanation:
If 1468 weren't in favor of the new park, then 3462-1468=1996 people were in favor of the new park. This means the percentage of those who are in favor of the park is 1996/3462=0.5765=57.65%=58%
Which of the following are solutions to the equation below?
2 cos^2 x – 1= 0
Answer:
no clue
Step-by-step explanation:
The Martins want to buy a new computer. The regular price is $849. The store is offering a 20% discount. What
is the total cost of the computer?
Answer:
679.20
Step-by-step explanation:
i used math plz mark branliest
Lance walked 20 miles east and then 21 miles north to get to work. If he walked back home after work using the most direct route, how many miles would he walk on the way back? (Find the hypoteneuse of the triangular path
Answer:
Solution given:
perpendicular [p]=20miles
base[b]=21Mile
hypotenuse [h]=?
we have
By using Pythagoras law
h²=p²+b²
h²=20²+21²
h=√841
h=29miles
he would walk 29 miles on the way back
will mark brainliest will mark brainliest
Answer:
1) SAS
2) SSS
3) SSA
4) ASA
5) No, not enough corresponding info given
Answer:
1) SAS
2) SSS
3) SSA
4) ASA
5) Sorry I don't know
Please mark me as the brainliest
if we added a 4th person to the race, what is the probability of the 4th person winning the race?
Answer:
1/4 chances
Step-by-step explanation:
its like rolling a dice. Six sides, Six different numbers, one will be picked
find the length of side x in simplest radical form with a rational denominator
Answer:
7
Step-by-step explanation
i did this
Lines AB and CD are parallel. If mZN is 52" then what is my?
A 128
B. 38
C. 142
D. 52
Elisa y su sombra forman un ángulo recto . La sombra anide 1,2 m y el ángulo con el que se ve la parte superior de su cabeza desde el extremo de la sombra mide 54° 50° . Calcular la altura de Elisa
Answer:
h = 1.65 m
Step-by-step explanation:
Me parece que el problema está mal formulado por lo siguiente:
El angulo al que se refiere el problema es 54° o es 50° o es 54°,50´
Como resolver el problema en cualquier caso.
Si Elisa y su sombra forman un angulo recto, entonces Elisa, su sombra y la distancia entre la cabeza de Eliza y el final de su sombra forman un triangulo rectangulo. Para el cual entonces solo es necesario buscar la tangente del angulo ( cateto opuesto sobre cateto adyacente) como conocemos el cateto adyacente ( la sombra de Elisa ) calculamos la altura de Elisa (h).
Asumamos que el angulo es de 54° entonces
tang 54° = 1.3763
tang 54° = 1.3763 = h/1.2
h = 1,3763*1,2 m
h = 1.65 m
De igual manera se procedería si el angulo es de 50° ( en este caso la tang 50° = 1.1917
Find the volume of a drum with a radius of 7 inches and a height of 15 inches
Answer:
pi*15*7^2=735pi=2309 (to the nearest whole number)
Find the area of a triangle with base of 10 inches and a height of 5 inches.
100 square inches
B 50 square inches
C) 25
square inches
D 12.5 square inches
Answer:
25 square inches
Step-by-step explanation:
just divide your base by 2 and then multiply it by the height
Does the question have no solution, one solution, or a infinite number of solutions?
2x + 3y = 6
2x + 3y = 7
Answer:
No solution
Step-by-step explanation:
I used this online calculator to find the answer. It shows the steps and everything. https://www.symbolab.com/solver?or=gms&query=2x%2B3y%3D62x%2B3y%3D7
Answer:
no solution
Step-by-step explanation:
Re-write the equation without the h component.
a. f(x)=2(3)^(x-2)+2
b. f(x)=1/2(4)^(x+1)
Answer:
[tex]f(x) = 2[\frac{3^x}{9}] + 2[/tex]
[tex]f(x) = 8(4)^x[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2(3)^{x-2} + 2[/tex]
[tex]f(x) = \frac{1}{2}(4)^{x+2}[/tex]
Required
Remove the h component
In a function, the h component is highlighted as:
[tex]f(x) = a^{x+h}[/tex]
So, we have:
[tex]f(x) = 2(3)^{x-2} + 2[/tex]
Split the exponents using the following law of indices:
[tex]a^m/a^n = a^{m-n}[/tex]
[tex]f(x) = 2*\frac{3^x}{3^2} + 2[/tex]
[tex]f(x) = 2*\frac{3^x}{9} + 2[/tex]
[tex]f(x) = 2[\frac{3^x}{9}] + 2[/tex]
The h component has been removed
[tex]f(x) = \frac{1}{2}(4)^{x+2}[/tex]
Split the exponent using the following law of indices
[tex]a^{m+n} =a^m * a^n[/tex]
So, we have:
[tex]f(x) = \frac{1}{2}(4)^x * 4^2[/tex]
Express 4^2 as 16
[tex]f(x) = \frac{1}{2}(4)^x * 16[/tex]
Divide 16 by 2
[tex]f(x) = 8(4)^x[/tex]
Six Less than four times a number is
-70
The answer is 286
Step-by-step explanation:
70 x 4 = 280 plus 6 equals 286
Please help me, I'm suffering from all of these parallel lines ;9
Only 1 is needed, but doing both would be godly <33
Answer:
1. y = 4x - 27
2. y = -4x - 15
Step-by-step explanation:
If two lines are parallel, then they have the same slope. So, the slope of the line we are looking for needs to be 4. We can start by writing a point-slope equation:
y - y1 = m(x - x1)
We can substitute the values we have, the point we are using is (8, 5) because it needs to be on the line:
y - 5 = 4(x - 8)
We can distribute:
y - 5 = 4x - 32
y = 4x - 27
We are not given the slope-intercept form, so we must divide both sides by two to get it:
y = 1/4 x + 8
A perpendicular line has the slope that is the negative reciprocal of the one that is given. So, the slope of the line would be - 4. We can start by writing a point-slope equation:
y - y1 = m(x - x1)
We can substitute the values we have, the point we are using is (-5, 5) because it needs to be on the line:
y - 5 = -4(x + 5)
We can distribute:
y - 5 = -4x - 20
y = -4x - 15
Jada can read 3/5 of an book in 1/4 of an hour How long would it take her to read one whole of the book
A.5/12 of a book per hour
B.5/12 of an hour per book
C. 2 and 2/5 books per hour
D.2 and 2/5 hours per book
Answer:
A)
Step-by-step explanation:
t = time to read whole book
(3/5 ÷ 1/4) = (5/5 ÷ t)
simplify:
12/5 = 1/t
cross-multiply:
12t = 5
t = 5/12
Simplify:
3x2 – 2x + 1 = [?]
x=4
Answer:
look at the picture i sent........
Please help! ASAP
I’m so confused
a parallelogram is transformed according to the rule (x , y)
Answer:
hi how are you doing today Jasmine
Use the compound interest formula to determine the final value of the given amount.
$150 at 3% compounded daily for 16 years.
The final value is $ ?
Answer:
342.22$
Step-by-step explanation:
What is one-half the sum of 142 and 8
Answer:
142+8=150
150/2=75
17. What is the value of C so that x^2+15x + c is a perfect square trinomial?
A. 30
B. 15/2
C. 15/4
D. 225/4
Answer:
D. 225/4
Step-by-step explanation:
To complete the square (a technique that can be applied to many problems!), take half the coefficient of x and square the result.
The coefficient of x is 15. Half of 15 is 15/2. Square 15/2 to get 225/4.
Check:
[tex]x^2+15x+\frac{225}{4}=\left(x+\frac{15}{2}\right)\left(x+\frac{15}{2}\right)=\left(x+\frac{15}{2}\right)^2[/tex]
Answer:
255/4
Step-by-step explanation:
A drink is available in 2 can sizes. Both have a diameter of 2 inches. The
small can has a height of 4 inches. The large can has a height of 6 inches.
Select all statements that are true:
The cans have the same volume.
The cans have the same circumference.
The small can has 2/3 the volume of the large can.
Both cans have a volume of more than 12 cubic inches.
Both cans have a volume of less than 18 cubic inches.
Answer:
Both cans have a volume of less than 18 cubic inches.
Step-by-step explanation:
please help me with my maths prep...........
Answer:
uumm
Step-by-step explanation:
PLEASE HELP W/ HONORS PROJECT! TIME SENSITIVE
What is the angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground? Show all of your work and round your answer to the nearest hundredth of a degree.
I know the degree but I need to know how the degree was found. I am using the U.S Cellular Field, aka the Guaranteed Rate Field in Chicago, IL.
The distance from the home plate to the center-field fence is 400 ft. The height of the center field fence is 8 ft. The given angle of elevation is 0.86 degrees.
Note:-
Solved as the all of above is one question
Solution:-
DE=8ft2 ft above
DE=10ftDF=400ftNow
Angle be x
Apply Pythagorean theorem
[tex]\\ \rm\Rrightarrow tanx=\dfrac{10}{400}[/tex]
[tex]\\ \rm\Rrightarrow tanX=\dfrac{1}{40}[/tex]
[tex]\\ \rm\Rrightarrow tanX= 0.025[/tex]
[tex]\\ \rm\Rrightarrow X=tan^{-1}(0.025)[/tex]
[tex]\\ \rm\Rrightarrow X=1.432°[/tex]
in a race, 19 out of 50 runners finished in fewer than 30 minutes. what percent of the runners finished in fewer than 30 minutes? Write and equivalent fraction to find the percent.
Answer:
8 Percent is: 32%
----
25
Step-by-step explanation:
Use the Parabola tool to graph the quadratic function.
f(x) = 2x2 + 16x + 31
Veronica has a box that contains 24 pictures of her family, 6 pictures of her dog, and 12 pictures of her friends. Veronica randomly chooses one picture from the box. Which statement best describes what will likely happen.
A. She will definitely pick a picture of her family
B. She will most likely pick a picture of her family
C. She is equally likely to pick a picture of her family or of her dog
D. She is equally likely to pick a picture of her family, of her dog or of her friends