Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {9}^{2} + {40}^{2} = {41}^{2} \\ 81 + 1600 = 1681 \\ 1681 = 1681[/tex]
In ΔDEF, the measure of ∠F=90°, DE = 9.4 feet, and EF = 8.4 feet. Find the measure of ∠D to the nearest degree.
Answer:
63°
Step-by-step explanation:
The sine of an angle is the ratio of the opposite side to the hypotenuse.
Sin = Opposite/Hypotenuse
sin(D) = EF/DE = 8.4/9.4
Using the inverse sine function, we can find the angle:
D = arcsin(8.4/9.4) ≈ 63.33°
∠D ≈ 63°
the length of a rectangle is 4 unit less than the width. which expression represents the perimeter of the rectangle
Answer:
Length: 11
Width: 5
Step-by-step explanation:
Let W = width
Let L = length
Length is 4 less than 3 times the width ==> L = 3*W - 4
Let P = Perimeter = 2*W + 2*L
Perimeter is 22 more than twice the width ==> P = 2*W + 22
Setting the 2 expressions for the perimeter equal to each other gives
2*W + 2*L = 2*W + 22
2*L = 22
L = 11
So 11 = 3*W - 4
3*W = 15
W = 5
The length is 11 and the width is 5
Check: 3*W - 4 = 11 = Length
Perimeter = 32 = 22 more than 2*5 = 10
PLEASE ANSWER I HAVE BEEN ON IT FOr A DARN HOUR
Answer:
-3
Step-by-step explanation:
The equation is y = -3 + .5x
Answer:
g(6) = 0, x = 6
Step-by-step explanation:
Sorry I forgot to look at the graph..
Graph is y = 1/2x - 3
Plug it in.
y = 1/2 (6) - 3
y = 0
A class of 64 students was given 320 book. How many will each student take home
Answer:
5
Step-by-step explanation:
320 / 64 = 5
What is the circumference of the following circle?
3 cm
Answer:
the circumference is 9.42 cm
Step-by-step explanation:
3.14 · (3 cm)
c = 9.42 cm
hope this helps :-)
Unit 8: Right Triangles & Trigonometry Homework 2: Special Right Triangles...Please Help!
Answer:
x = 8√3y = z = 12√2Step-by-step explanation:
We presume you want the values of x, y, and z.
__
There are two "special triangles" in geometry and trigonometry. They are the 30°-60°-90° right triangle that is half of an equilateral triangle, and the 45°-45°-90° isosceles right triangle that is half a square (cut by the diagonal).
The side ratios of these special triangles are relatively easy to remember. It is useful to memorize them.
__
For the isosceles right triangle, the side lengths are the same. The Pythagorean theorem tells you that if they are both 1, then the hypotenuse is ...
√(1²+1²) = √2
That is, the side lengths of the 45-45-90 triangle are in the ratio ...
1 : 1 : √2
__
For the triangle that is half an equilateral triangle, you know the hypotenuse is twice the length of the shortest side (since we got that short side by cutting a long side in half). Then the longer side can be found from the Pythagorean theorem:
√(2²-1²) = √3
That is, the side lengths of the 30-60-90 triangle are in the ratio ...
1 : √3 : 2
_____
In this problem, we're given the hypotenuse of a 30-60-90 triangle, so we know the short side of it (x) will be half that length:
x = (16√3)/2
x = 8√3
The hypotenuse of the 45-45-90 triangle will be √3 times x, so will be ...
long side of small triangle = (√3)(8√3) = 24
The shorter sides of that 45-45-90 triangle will be this value divided by the square root of 2, so are ...
y = z = 24/√2
We can multiply this by (√2)/(√2) to "rationalize the denominator".
y = z = 12√2
Answer:
8\sqrt{3},\ 12\sqrt{2},\ 12\sqrt{2}
Step-by-step explanation:
Mr. Hernandez combines 1 gallon of orange juice, 3 pints of pineapple juice, and 2 quarts of lemon-lime soda to make punch for a party. He allows 2 cups of punch for each guest. Will there be enough punch to serve all 14 guests? How much, if any, punch will be left
Answer:
1 . There will be enough cup of punch to serve all 14 guest
2. There will be 2 cups of punch left.
Step-by-step explanation:
Mr Hernandez combines 1 gallon of orange juice, 3 pint of pineapple juice and 2 quarts of lemon-lime soda to make punch for a party.
This combination makes up the punch. We have to convert to cups to ascertain if the punch will be enough to serve 14 guest which are entitle to 2 cups of punch. The 14 guest will consume a total of 28 cups of punch .
1 gallon of orange juice = 16 cups of orange juice
1 pint = 2 cups
3 pints of pineapple = 6 cups
1 quarts = 4 cups
2 quarts of lemon-lime soda = 8 cups
When you combine all the cups together, the total punch will be = 16 + 6 + 8 = 30 cups of punch.
The guest will consume a total of 14 × 2 = 28 cups of punch. There will be 30 - 28 = 2 cups of punch left.
The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.12 kWh. A previous study found that for an average family the standard deviation is 1.2 kWh and the mean is 17.9 kWh per day. If they are using a 90% level of confidence, how large of a sample is required to estimate the mean usage of electricity? Round your answer up to the next integer.
Answer:
A sample size of at least 271 is required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Maxium error of 0.12.
How large of a sample is required to estimate the mean usage of electricity?
We need a sample size of at least n.
n is found when [tex]M = 0.12, \sigma = 1.2[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.12 = 1.645*\frac{1.2}{\sqrt{n}}[/tex]
[tex]0.12\sqrt{n} = 1.645*1.2[/tex]
[tex]\sqrt{n} = \frac{1.645*1.2}{0.12}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645*1.2}{0.12})^{2}[/tex]
[tex]n = 270.6[/tex]
Rounding up
A sample size of at least 271 is required.
what is the volume of one cube with an edge length of 1/4 inch?
Answer:
(1/64) in^3, or 0.015625 in^3
Step-by-step explanation:
The formula for the volume of a cube of side length s is V = s^3.
Here, with s = 1/4 in,
V = (1/4 in)^3 = (1/64) in^3, or 0.015625 in^3
Concession Stand Prices. A bag of chips is 50 cents, apple is 20 cents, sandwich is 1 dollar, and juice box is 75 cents.
Erica is working the concession stand. She sold 6 bags of chips, 14 apples, and 3 juice boxes. She has $12.05 in the cash register. How many sandwiches has she sold?
3 sandwiches
4 sandwiches
5 sandwiches
6 sandwiches
Answer:
4
Step-by-step explanation:
bet
Answer:
The Answer is 4 on Edg
Step-by-step explanation:
Mhm
parker spends 1/4 of his earnings on rent and 1/6 of his earnings on entertainment
Answer:
Cool
Step-by-step explanation:
the sum of three consecutive numbers is 114 . what is the smallest of these numbers
Answer:
x + (x+1) + (x+2) = 114
3x = 111
x = 37
the numbers are 37, 38 and 39
the smallest number is 37
Step-by-step explanation:
Why equals 3/4 X -12 and why equals negative 4X - 31
Answer:
(x, y) = (-4, -15)
Step-by-step explanation:
Perhaps you want the solution to ...
y = 3/4x -12
y = -4x -31
Equating the two expressions for y gives ...
3/4x -12 = -4x -31
3/4x = -4x -19 . . . . . add 12
3x = -16x -76 . . . . . multiply by 4
19x = -76 . . . . . . . . . add 16x
x = -76/19 = -4 . . . . divide by 19
y = (3/4)(-4) -12 = -15 . . . . use the first equation to find y
The solution to this system of equations is ...
(x, y) = (-4, -15)
What is the sum in simplest form I ready diagnostic please hurry
example:
The value of x is 22
Step-by-step explanation:
We are given that there are two numbers
First number is x
second number is 35
The sum of x and 35 is 57
so, we get equation as
now, we can solve solve x
So, subtract both sides by 35
What’s the correct answer for this?
Answer:
B
Step-by-step explanation:
In the attached file
For the arithmetic sequence beginning with the terms {9, 14, 19, 24, 29, 34 ...}, what is the sum of the first 23 terms?
Answer:
1472
Step-by-step explanation:
The sum of n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = 19 - 14 = 5 , thus
[tex]S_{23}[/tex] = [tex]\frac{23}{2}[/tex] [ (2 × 9) + (22 × 5) ]
= 11.5 (18 + 110) = 11.5 × 128 = 1472
A national survey of companies included a question that asked whether the customers like the new flavor of a cola from company A. The sample results of 1000 customers, and 850 of them indicated that they liked the new flavor. The 98% confidence interval on the population proportion of people who like the new flavor is _______________.
Answer:
The 98% confidence interval on the population proportion of people who like the new flavor is (0.8237, 0.8763).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1000, \pi = \frac{850}{1000} = 0.85[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.85 - 2.327\sqrt{\frac{0.85*0.15}{1000}} = 0.8237[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.85 + 2.327\sqrt{\frac{0.85*0.15}{1000}} = 0.8763[/tex]
The 98% confidence interval on the population proportion of people who like the new flavor is (0.8237, 0.8763).
I need help with this.
Answer:
6
Step-by-step explanation:
1.5*4=6
To solve this problem, we'll set up a ratio between the equivalent values.
We know that 1 1/2 pages and 1/4 of an hour are our two values, and assuming that Azi writes at a constant speed, we're able to write this ratio:
1.5 : .25
(I'm just writing with decimals because I find them easier to work with, but decimals or fractions will give you the correct answer.)
Since .25 is 1/4 of an hour, we can multiply this value by 4 to get 1 hour.
Additionally, since this is a ratio, what you do to one side must be done to the other, so 1.5 will also be multiplied by 4.
(1.5 x 4) = (.25 x 4)
6 = 1
Therefore, Azi can type 6 pages in one hour.
Hope this helped! :)
Pls answer I give brainliest thank you! Number 4
Answer:
6
Step-by-step explanation:
I did the work but like where did that cube go lol
Answer:
1/6 would be the answer because you multiply
1/2 x 1/2 x 1/2 = 1/6
5. 2 by 2 by 1 would work
Step-by-step explanation:
Mia has a rectangle shape brownie. She cuts the brownie into 3 equal pieces.Which sentence is true ?
Answer:
The whole brownie is 3/3
Step-by-step explanation:
Hello!
This is a classic fractions exercise.
The whole brownie was cut in three equal pieces. Each piece represents 1/3 of the brownie.
If you add the three pieces together 1/3+1/3+1/3 you get the whole brownie again 3/3 = 1
-Options-
The whole brownie is 1/3.
The whole brownie is 3/3.
The whole brownie is 2/3.
The whole brownie is 3/2.
I hope this helps!
Find the area of a semi-circle with radius, r = 83cm.
Give your answer rounded to 1 DP.
Hannah is setting up chairs for the class play. The room has 20 chairs. What are the different ways she can arrange the chairs in a rectangle?
Answer:
Have them 4 by 5.
Step-by-step explanation:
If you she but 5 chairs in a row, then 3 on the side of the chairs. That would create a backward "L" type of shape.
For example, (The "o" is a chair)
OOOOO
O
O
O
As you see the the top are the 5 chairs, then side are are the 4 chairs.
Then, you will do the exact same thing but on the opposite side.
Here is the next example.
OOOOOO
O O
O O
O O
OOOOOO
Basically, arranging the chairs 4x5, it would make a rectangle.
100 POINTS TO ANSWER THIS PLZ HURRY
Answer:
This is tricky but I think it is A.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Simplifying products and quotients of powers
7^2•7^8/7^4=7^a/7^4=7^b
A=
b=
Answer:
a=10
b=6
Step-by-step explanation:
add 2 to 8, to get a, then subtract 4 from 10 to get b
Answer:
10 and 6
Step-by-step explanation:
if a cube measures 5.3 cm on each side and has a mass of 280 grams how much is its volume
Answer:
8.1 g/cm
Step-by-step explanation:
What is the solution to this system of equations 3x+y=17 and x+2y=49
Answer:x=-3 y=26
Step-by-step explanation:
3x+y=17.............(1)
x+2y=49..............(11)
From (11) x=49-2y
Substitute x=49-2y in 3x+y=17
3(49-2y) + y=17
Open bracket
147-6y+y=17
147-5y=17
Collect like terms
5y=147-17
5y=130
Divide both sides by 5
5y/5=130/5
y=26
Substitute y=26 in x+2y=49
x+2(26)=49
x+52=49
Collect like terms
x=49-52
x=-3
Answer:
It has a single solution: x = -3, y = 26.
Step-by-step explanation:
Mariska was comparing her options for investment. One choice she was looking at showed that her principal of $1,875 over 10 years would
earn $1,125 in interest giving her a total of $3,000 at the end of the investment period. What interest rate is being used to calculate this
Investment?
solve for x. x+y = 14
Answer:
There is not enough information to specifically tell you the amount for x
Answer:x=14-y
Step-by-step explanation:
x+y=14
x=14-y
Which equation represents a line that has a slope of 1/3 and passes through point -2, one
Answer: y= 1/3 x + 5/3
Step-by-step explanation:
1= 1/3(-2) + b where b is the y intercept
1= -2/3 + B
+2/3 +2/3
B = 5/3
so we know the slope and the y- intercept
y= 1/3x + 5/3 check: 1=1/3(-2) +5/3
1 =1
Slope intercept form: y = mx + b
m = slope
b = y-intercept
Since we know the slope and one point, we can solve for the y-intercept.
y = 1/3x + b
1 = 1/3(2) + b
1 = 2/3 + b
1 - 2/3 = 2/3 - 2/3 + b
1/3 = b
Now, put the final equation together.
y = 1/3x + 1/3
Best of Luck!
Can someone help me with this
Answer:
(y-b) /x = m
Step-by-step explanation:
y = mx+b
Subtract b from each side
y -b = mx+b-b
y-b = mx
Divide each side by x
(y-b) /x = mx/x
(y-b) /x = m
