Answer:
900
Step-by-step explanation:
Given that :
Enrollment declined by 20% from between September 1991 to September 1994
This means there was a reduction in enrollment ;
Enrollment in September 1994 = 720
Enrollment in September 1991 = x
Hence,
Enrollment in 1994 = (1 - decline rate ) * enrollment in 1991
720 = (1 - 20%) * x
720 = (1 - 0.2) * x
720 = 0.8x
720 / 0.8 = 0.8x/0.8
900 = x
Hence, Enrollment in September 1991 = 900 enrollments
expresión algebraica el cuadrado del cubo de la suma de dos números
Answer:
El cuadrado de la suma de dos números es igual a (a + b) ² = a² + 2ab + b²Un producto notable: es una expresión matemática que conocemos ya el resultado, a pesar de la operación ser sencilla tenemos
Please help out explanation need it
For this you just look at the sides.
Soh cah toa
This is good to remember.
Sin = opposite/ hypotenuse
Cos= adjacent/ hypotenuse
Tan = opposite/ adjacent
In this case you have TanZ, the side adjacent to the angle is 10 and the opposite to the angle is 24. So tanZ is 24/10 which simplifies to 12/5.
The hypotenuse is always the longest side, but the opposite and adjacent sides can change depending on the angle.
Answer:90 = ... 42 + 48) - 360
Step-by-step explanation:
The critical value of F for an upper tail test at a 0.05 significance level when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is _____. a. 2.94 b. 2.45 c. 2.10 d. 2.37
Answer:
2.45
Step-by-step explanation:
Given that :
α = 0.05
Larger sample variance= numerator, sample size = 9
Smaller sample variance = denominator, sample size = 21
Hence,
DFnumerator = n - 1 = 9 - 1 = 8
DFdenominator = n - 1 = 21 - 1 = 20
Critical value for upper tail test using the F distribution table at α = 0.05 ; DFnumerator on horizontal ; Df denominator as vertical ;
F critical = 2.447
F critical = 2.45
ANSWER NOW IM TIMED Louie uses 10 feet of wood, 16 wheels and one can of paint for every 4 skateboards he builds.
A 4-column table with 3 rows. Column 1 is labeled Skateboards with entries 1, 4, 10. Column 2 is labeled Wood with entries blank, 10 feet, blank. Column 3 is labeled Wheels with entries blank, 16, blank. Column 4 is labeled paint with entries blank, 1 can, blank.
Use the table to find how much of each item Louie needs to build 10 skateboards.
Louie needs
feet of wood,
wheels, and
cans of paint.
Answer: 25 feet of wood
40 wheels and 2.5 cans of paints
Step-by-step explanation:
Answer:
25 feet of wood
40 wheels and
2.5 cans of paints
Step-by-step explanation: I did this before Also can i get brainlyist please
which of the following statements is true? -6 < -8 -6> -8 or -6=-8
Answer:
-6>-8
Step-by-step explanation:
-6 is more than -8.
The figure below is a net for a right rectangular prism. Its surface area is 104 ft2 and
the area of some of the faces are filled in below. Find the area of the missing faces,
and the missing dimension.
Answer:
12+12+10+10=44
104-44=60
60÷2=30
30 is the surface area of A
30÷6=5
5 is a missing dimention
What are the zeros of f(x) = x^2 - x - 12?
A. x= -4 and x= 3
B. x=-3 and x = 4
C. x=-2 and x = 6
D. x=-6 and x = 2
Answer:
B. x = -3 and x = 4
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringSolving quadraticsStep-by-step explanation:
Step 1: Define
Identify
f(x) = x² - x - 12
Step 2: Solve for x
Factor: (x - 4)(x + 3) = 0Solve: x = 4, -3Find the distance between the two points (1.5,2.7) and (3.5,4.3) given in polar coordinates and using radians.
Answer:
2.56
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(3.5 - 1.5)² + (4.3 - 2.7)²
√(2)² + (1.6)²
√(4) + (2.56)
√6.56
= 2.56
Rope pieces of lengths 45 cm, 75 cm and 81 cm have to be cut into same size pieces. What is the smallest piece length possible?
Answer:
2025 cm
Step-by-step explanation:
Given the length of pieces - 45 cm, 75 cm and 81 cm
To find the length of the rope we have to find the L.C.M. of 45, 75 and 81 :
3 | 45, 75, 81
| ________________
3 | 15, 25, 27
|________________
3 | 5, 25, 9
|________________
3 | 5, 25, 3
|________________
5 | 5, 25, 1
|________________
5 | 1, 5, 1
|________________
| 1, 1, 1
L.C.M. = 3 × 3 × 3 × 3 × 5 × 5
= 2025 cm
So, the least length of the rope should be 2025 cm which can be cut into a whole number of pieces of length 45 cm, 75 cm and 81 cm.
What is the volume of this regular prism?
54.97 cubic inches
8.91 cubic inches
109.95 cubic inches
21.99 cubic inches
Answer:
A
Step-by-step explanation:
The volume of prism is b*h, base area is (2.5)*(3.24*(1.1)=8.91. Hence volume is 8.91*6.17=54.97
Which function is graphed?
(Help please)
Answer:
the function that is graphed is y=½CSC(x)
Help I have a time limit
Answer:
I think its C:37
Step-by-step explanation:
And if im wrong sorry :/
find the area of the shaded region
Answer:
22 cm²Step-by-step explanation:
Shaded area is the difference of the bigger circle and two smaller ones:
A = π(3²) - 2π(1²) = 7π = 7*3.14 ≈ 22 cm²Determine the indicated term in the following arithmetic sequences.
1.) a subscript 5: {2, 5, 8, ...}
2.) a subscript 20: {4, 8, 12, ...}
3.) a subscript 18: {0,20,40,60, ...}
Answer:
[tex]a_5= 14[/tex]
[tex]a_{20}= 80[/tex]
[tex]a_{18}= 340[/tex]
Step-by-step explanation:
Solving (a):
We have:
[tex]a_1=2[/tex] --- first term
[tex]d = 5 -2 = 3[/tex] common difference
The 5h term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_5= 2+ (5 - 1)*3[/tex]
[tex]a_5= 14[/tex]
Solving (b):
We have:
[tex]a_1 = 4[/tex] --- first term
[tex]d = 8 -4 = 4[/tex] common difference
The 20h term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_{20}= 4+ (20 - 1)*4[/tex]
[tex]a_{20}= 80[/tex]
Solving (c):
We have:
[tex]a_1 = 0[/tex] --- first term
[tex]d = 20 -0 = 20[/tex] common difference
The 18th term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_{18}= 0+ (18 - 1)*20[/tex]
[tex]a_{18}= 340[/tex]
Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows.
Before 13 22 65 123 56 63
After 14 21 43 84 75 72
1. The article included the statement "A paired t-test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs." Carry out such a test. (Note: The relevant normal probability plot shows a substantial linear pattern.)
a. State and test the appropriate hypotheses. (Use α = 0.05.)
b. Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t = _____
p-value = _____
c. State the conclusion in the problem context.
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
B. Reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
C. Fail to reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
D. Reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
2. If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in the number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)
Answer:
Test statistic = 0.63
Pvalue = 0.555
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
Step-by-step explanation:
Given :
Before 13 22 65 123 56 63
After_ 14 21 43 84 75 72
To perform a paired t test :
H0 : μd = 0
H1 : μd ≠ 0
We obtain the difference between the two dependent sample readings ;
Difference, d = -1, 1, 22, 39, -19, -9
The mean of difference, Xd = Σd/ n = 33/6 = 5.5
The standard deviation, Sd = 21.296 (calculator).
The test statistic :
T = Xd ÷ (Sd/√n) ; where n = 6
T = 5.5 ÷ (21.296/√6)
T = 5.5 ÷ 8.6940555
T = 0.6326
The Pvalue : Using a Pvalue calculator ;
df = n - 1 = 6 - 1 = 5
Pvalue(0.6326, 5) = 0.5548
Decision region :
Reject H0 ; If Pvalue < α; α = 0.05
Since 0.5548 > 0.05 ; we fail to reject the Null and conclude that the data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
There is a language with 12 distinct letters. How many words that are less than four letters long can possibly be formed? (Assume any combination of letters is valid and letters can be repeated). Can you help me out with this one?
Answer:
1884
Step-by-step explanation:
1)If you hear the condition "less than four letters" it means that each word can consist of 3,2 or 1 letter. Firstly, consider the easiest situation with the word from one letter. There are 12 letters, so there are 12 words from one letter.
Then the words from two letters. The first letter of such a word can be chosen in 12 means(because 12 letters are available), then the second letter can be chosen in 12 means too. 12*12=144 words with 2 letters. (Multiplying, not adding, because each two words form one combination).
Then for the words from three letters, use the same rule, 12 means for the first letter, 12 means for the second letter, 12 means for the third letter. 12*12*12=1728 words.
Having particular words from 1,2,3 letters add them to get total quantity of words: 12+144+1728=1884words,that is the answer.
There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of exactly 1 red?
please need ASAP
Answer:
3 out of 12 chance i believe.
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
We'll need to use casework, since the problem stipulates there needs to be exactly one red drawn. Because we're drawing two marbles, we can either draw a red one first or a red one second. With casework, we'll add the probability a red marble is drawn the first draw and the probability a red marble is drawn the second draw.
There are [tex]4+3+5=12[/tex] marbles total. The probability of drawing a red marble is equal to the number of red marbles (3) divided by the total number of marbles (12). Therefore, the probability of getting a marble on the first draw is [tex]3/12=1/4[/tex]. Since the marble is replaced, there are still 12 marbles, 4 blue, 3 red, and 5 green, for the second draw. We want to add the probability a red marble is drawn the first draw to the probability a red marble is drawn the second draw. Therefore, for the second draw, let's find the chances of not choosing a red marble. There is a [tex]9/12[/tex] chance that the marble chosen is not red. Therefore, the probably of this case happening is [tex]\frac{1}{4}\cdot \frac{9}{12}=\frac{9}{48}[/tex].
This case has the exact same probability as the other case, where a non-red marble is chosen the first draw and the red marble is now chosen the second draw ([tex]9/12[/tex] chance to choose a non-red marble and [tex]1/4[/tex] chance to choose a red marble).
Add these cases up:
[tex]\frac{9}{48}+\frac{9}{48}=\frac{18}{48}=\boxed{\frac{3}{8}}[/tex]
Use the Pythagorean Theorem to find the length of the indicated side of the following right triangle. (NOTE: The square-like symbol indicates a 90-degree angle.)
Pythagorean Theorem: a^2 + b^2 = c^2
a = 5
b = ?
c = [tex]\sqrt{61}[/tex]
5^2 + b^2 = ([tex]\sqrt{61}[/tex])^2
25 + b^2 = 61
b^2 = 36
b = 6
Hope this helps!
(Use Pascal's triangle to expand each binomial. (x – 5y)^5
The n-th row in Pascal's triangle tells you the coefficients of terms in the expansion of (a + b)ⁿ. Starting with n = 0,
1
1 … 1
1 … 2 … 1
1 … 3 … 3 … 1
1 … 4 … 6 … 4 … 1
1 … 5 … 10 … 10 … 5 … 1
In more concrete terms, this translates to
(x - 5y)⁵ = 1 x ⁵ (-5y)⁰ + 5 x ⁴ (-5y)¹ + 10 x ³ (-5y)² + 10 x ² (-5y)³ + 5 x ¹ (-5y)⁴ + 1 x ⁰ (-5y)⁵
Simplify:
(x - 5y)⁵ = x ⁵ - 25x ⁴y + 250x ³y ² - 1250x ²y ³ + 3125xy ⁴ - 3125y ⁵
Date Page If the product of two identical number is 1024, find one of the numbers
Answer:
32
Step-by-step explanation:
Let the number be x^2.
x^2 =1024
x = √1024
x = 32
Answer:
32, 32
Step-by-step explanation:
x * x = 1024
x² = 1024
x = √1024
x = 32
A study was done to determine the average number of homes that a homeowner owns in his or her lifetime. For the 50 homeowners surveyed, the sample average was 5.1 and the sample standard deviation was 3.8. Calculate the 95% confidence interval for the true average number of homes that a person owns in his or her lifetime.
Answer:
The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0096
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0096\frac{3.8}{\sqrt{50}} = 1.1[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 5.1 - 1.1 = 4
The upper end of the interval is the sample mean added to M. So it is 5.1 + 1.1 = 6.2.
The 95% confidence interval for the true average number of homes that a person owns in his or her lifetime is (4,6.2).
Extraneous solutions are answers that don't work and/or produce division by zero.
True
False
Find the area of the shaded part !
Answer:
Step-by-step explanation:
Semicircle:
Shaded area of semicircle = area of outer semicircle - area of inner semicircle
Outer semicircle:
d = 40 m r = 40/2 = 20m
Area of outer semicircle = πr²
= 3.14*20*20
= 1256 m²
Inner semicircle:
d = 30 m r = 30/2 = 15 m
Area of outer semicircle = πr²
= 3.14*15*15
= 706.5 m²
Shaded area of semicircle = 1256 - 706.5 = 549.5 m²
Shaded area of semicircle in both sides = 2 * 549.5 = 1099 m²
Rectangle on both sides:
Length = 50 m
width = 30 m
Area of shaded rectangles on both sides = 2* (length *width)
= 2* 50 * 30
= 3000 m²
Shaded area = 1099 + 3000 = 4099 m²
A triangle is rotated 90° about the origin. Which rule describes the transformation?
(x, y) (-x, -y)
O(x,y) (-y, x)
(x, y) (-), -x)
(x,y) →ly, -x)
Answer:
(x,y) -> (-y,x), second option.
Step-by-step explanation:
Rotation of 90 degrees about the origin:
The rule for a rotation of a point (x,y) 90 degrees about the origin is given by:
(x,y) -> (-y,x)
This is that the question asks, and so, this is the answer, which is the second option.
Will give brainliest
A tablet at a local electronics store is in high demand and will only be available to customers for a limited time. The store initially has 4 cases of the tablet on hand. The store manager receives new supplies of the tablet each week. At the beginning of week 1, the store manager receives an additional order from the distributor of 5 cases of tablets. At the beginning of week 6, the manager receives another order of 10 cases. Which of the following equations best models the scenario for how many cases of the tablet the store can expect to receive each week?
a. y=4
b. y=x+4
c. y=-6x
What is the product of (2x - 5)(2x + 5)2 ?
Find the area of the shaded region in the image below:
9514 1404 393
Answer:
34 square units.
Step-by-step explanation:
The figure can be decomposed into a trapezoid and a triangle. The point of intersection of the two lines is (6, 4), so a horizontal line at y=4 will create ...
a triangle of height 2 and base 6a trapezoid with bases 6 and 8, and height 4.Using the relevant area formulas, we find ...
triangle area = 1/2bh = 1/2(6)(2) = 6
trapezoid area = 1/2(b1 +b2)h = 1/2(6+8)(4) = 28
Total shaded area = 6 + 28 = 34 square units.
__
The equations of the lines can be written as ...
y = -2x +16
y = -1/3x +6
Equating y, we get
-2x +16 = -1/3x +6
10 = 5/3x . . . . . . . . . add 2x-6
6 = x . . . . . . . . . multiply by 3/5
y = -2(6) +16 = 4
The point of intersection is (6, 4).
_____
Alternate solution
Once we know the vertices of the shaded area:
(0, 0)(0, 6)(6, 4)(8, 0)(0, 0)we can form pairwise "determinants" of the form x1y2 -x2y1. Note the first point is repeated at the bottom of the list, and the points are listed in order around the boundary of the area. The points (0, 0) contribute nothing, so we have left them out of the computation below. The area is half the absolute value of the sum of these "determinants".
1/2|(0·4 -6·6) +(6·0)-(8·4)|
= 1/2|-36 -32| = 1/2(68) = 34
_____
In the attachment, the equations of the lines are written in intercept form, since the problem statement gives the intercepts of the lines.
The three numbers in an AP whose sum is 27 and the sum of their squares is 341 are
Answer:
this and that and that is this
Step-by-step explanation:
step by step
Political Stcibility
Answer:
Political stability is a variable of great importance in a country's evolution since, across time, it was identified as causing law level of economic growth, but also it was presented as a consequence of poor economic development.
CAN SOMEBODY HELP WITH THIS QUESTION ASAP
Answer:
The rectangles are not similar
Step-by-step explanation:
In order to check whether they are similar, we need to take the ratio of their similar sides and ensure they are equal to a constant k.
Hence;
AB/PL = AD/LM = k
32/26 = 18/12 = k
16/13 = 9/6 = k
Since the scale factor is not the same, hence the rectangles are not the same.
