Answer:
[tex]S_{1000}=500500[/tex]
Step-by-step explanation:
[tex]\displaystyle S_n=\frac{n(a_1+a_n)}{2}=\frac{1000(1+1000)}{2}=500*1001=500500[/tex]
The Board of Education (DOE) claims that the average salary of substitute teachers in school
district in Nassau County, NY, is about $175 per day. A random sample of 6 school districts is
selected, and the daily salaries (in dollars) are collected into calculation with sample mean is $80
and sample standard deviation is 6.3. Calculate at α = .05 significance level whether the true
mean greater than $175.
Please explain step by step and as clear as possible
The null hypothesis is rejected.
The mean is not greater than $175.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
Sample size (n) = 6
Sample mean ([tex]\bar x[/tex]) = $80
Sample standard deviation(s)=6.3
Significance level(α)=0.05
We have to test the claim that the true mean greater than $175.
The null and alternative hypotheses:
H₀ : μ = 175
H₁ : μ > 175
Here, Population Standard deviation is unknown and sample size is less than 30.
So we will use t- distribution.
Test Statistic t,
t = ([tex]\bar x[/tex] - μ) / {s/√n}
t = (80−175) / (6.3 /√6)
t = (80−175) / (6.3 / 2.45)
t = − 95 / 2.57196423
t = −36.937
degree of freedom (df) = n−1
= 6−1
= 5
p-value at t = −36.937, df = 5 and α = 0.05
Absolute value of −36.937 = 36.937
Notice that 36.937 does not show up in the table, but it does fall between the two values 31.821 and 63.657.
So, p-value = 1
Since, p-value > α
That means, we fail to reject the null hypothesis (H₀).
Therefore, the true mean is not greater than $175.
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A kite is flying 24 ft off the ground. Its line is pulled taut and casts a 7-ft shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.
The side lengths are;
tan x = e/f
cos x = e/d
sin x = f/d
What is a right angled triangle?We know that a right angled triangle is the kind of triangle that one of the sides of the triangle would be 90 degrees.
There are some ratios that are associated with the right angled triangle and we call them the trigonometric ratios. These include the sine the cosine and the tangent. All of these ratios does depend on the lengths of the sides of the right angled triangle.
The sides of the right angled triangle are the opposite, the adjacent and the hypotenuse and these can be obtained based on the relative position of the angle.
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Five people each working eight hours a day can assemble 400 toys in a five day work week. What is the average number of toys assembled per hour per person?
Answer:
There are 5 people working and each person works 8 hours per day, so there are a total of 58 = <<58=40>>40 hours of work per day.
Over the course of the week, the total number of hours worked is 405 = <<405=200>>200 hours.
The total number of toys assembled is 400 and the total number of hours worked is 200, so the average number of toys assembled per hour per person is 400/200 = <<400/200=2>>2 toys per hour per person. Answer:{2}.
Step-by-step explanation:
If the sun is 57 degrees above the horizon, find the length of the shadow cast by a building 56 ft tall. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
The Length of shadow is 35.56 ft.
Given that,
If the sun is 68° above the horizon.
Based on the above information, the calculation is as follows:
tan68° =BC divide AC
tan68° =88 divide b
b =88 divide tan68°
=88 divide 2.475
= 35.56 ft.
express 1.21 as percent
Answer: 121%
Step-by-step explanation:
move the decimal place two to the right
For brainliest and 50 points!!!
The statements in if-then form are given as follows:
If it is right-angled, then it is 90 degreesIf x=6, then x² = 36If two angles measure 180°, then they are supplementary If your body temperature is 103°, then you have a fever If is 6pm, then it is time for dinnerIf there is gas in the tank, then the car runs If there there are 12 eggs if the carton, then it is fullIf a car is leaking antifreeze, then it has a problemIf a dog is old, then you can't teach it new tricksIf a deer has white fur and pink eyes, then it is albino What is the value of an IF-Then Construct?If-Then statements are a sort of variable logic that allows the variable's output to be determined conditionally. All If-Then statements must specify the circumstances and actions that should occur when those criteria are fulfilled.
If-then arguments, also known as conditional arguments or hypothetical syllogisms, are deductive logic's workhorses. They are a loosely defined class of logical arguments with an if-then statement (a conditional) as a premise. The conventional form of the conditional is If P, Q follows.
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Given f(x) = -3x + 1, solve for a when ƒ(x) = −5.
Clearly f(x) is one-one onto function so it is invertible so ƒ(x) is y + -5 /3.
What one-one onto function ?Each element of one set, let's say Set (A), is mapped with a particular element of another set, let's say Set (B), where A and B are two separate sets. This is known as a one-to-one function or one-to-one mapping. 1-1 is another way to write it. If f(x) = f(y) means that x = y, then f is one to one in terms of function.
Let y = f(x) = -3x + 1
Clearly f(x) is one-one onto function so it is invertible.
⇒y = -3x − 1 ⇒ x = y+1 /-3
∴f (x)= -5
y + -5 /3
Clearly f(x) is one-one onto function so it is invertible so ƒ(x) is y + -5 /3
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3. Candy previously sold for $1.60 per pound is now offered for 48 cents in a 6 ounce
package. What is the ratio of former price to present price??
Answer: 5:3
Step-by-step explanation:
note: 16 ounces= one pound
6 ounces = ?
∴6 ounces = pounds
48 cents = pounds
multiplying both sides by
108 cents = 1 pound in the new price
= $1.08 in the new price
ratio of old price to new price =
therefore ratio of old to the new price = 5:3
The temperature at a mountain cabin on
Saturday morning measured -12 degrees
Fahrenheit. The temperature decreased
another 8 degrees Saturday night. In
degrees Fahrenheit, what was the
temperature at the cabin Saturday night?
G-12 H 12
F -20
J -4
On Saturday night, the temperature at the mountain cabin decreased another 8 degrees from -12 degrees Fahrenheit, so the temperature at the cabin on Saturday night was -12 degrees - 8 degrees = -20 degrees Fahrenheit.
help me with this please
Pls help fractions pls and sm else
Answer:
Step-by-step explanation:
(49/72)-(13/14)
-125/504
"what is the median of the following values 9,9,2,8,11,6,4"
Answer: 8
Step-by-step explanation:
Arrange the data in ascending order, and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
Rearrange 9, 9, 2, 8, 11, 6, 4 in ascending order:
2, 4, 6, 8, 9, 9, 11
The number eight appears to be in the very middle, therefore it is the median.
Which of these ratios are equivalent? Choose all that apply.
1) 16:4
2) 2:1
3) 32:2
4) 480:120
5) 4:16
6) 4:1
The ratios which are equivalent are as follows:
1) 16:4
4) 480:120
6) 4:1
Step-by-step solution:
1) 16:4
[tex]=\frac{16}{4}[/tex]
[tex]=\frac{4}{1}[/tex]
4:1
2) 2:1
[tex]=\frac{2}{1}[/tex]
2:1
3) 32:2
[tex]=\frac{32}{2}[/tex]
[tex]=\frac{16}{1}[/tex]
=16:1
4) 480:120
[tex]=\frac{480}{120}[/tex]
[tex]=\frac{4}{1}[/tex]
=4:1
5) 4:16
[tex]=\frac{4}{16}[/tex]
[tex]=\frac{1}{4}[/tex]
=1:4
6) 4:1
[tex]=\frac{4}{1}[/tex]
=4:1
Therefore, the correct solution to this question is:
1) 16:4
4) 480:120
6) 4:1
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Answer:
16:4 and 480:120 and 4:1 are equivalent.
Step-by-step explanation:
carmela translates f (x) = x2 to create p (x). If p 9 (x) = f (x+3) -10 sketch the graph
The function p(x) = (x + 3)² is transformed 3 units left along the x-axis.
What are some rules of function transformations?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over the x-axis, (x, -y).
Given, A function f(x) = x².
Now, p(x) = f(x + 3).
p(x) = (x + 3)² and it is a transformed function to the parent function f(x).
Now, The function p(x) = (x + 3)² is transformed 3 units to the left along the x-axis.
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F(x)=2 sin (1/2x)+1
What is the midline of the functionless
Answer: 4
Step-by-step explanation:
Let me get to know you:)
Which graph represents a function?
P
Edet took sixth at the end of term test and each test was marked out of 80. If his marks were 48, 52, 46, 46, 44 and 52. What percentage of the total marks did he get?
The percentage of the total marks that Edet gets is 60%
How to calculate the percentage?The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this situation, the score of Edet will be:
= 48 + 52 + 46 + 46 + 44 + 52
= 288
Total score = 80 × 6
= 480
The percentage will be:
= 288 / 480 × 100
= 60%
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Angelina has taken 27 of the 36 exams she needs to take to become a nurse. What percent of the exams has she taken?
The percentage of the exam that she has taken is 75%.
What percentage of the exam has she taken?Percentage is a measure of frequency that is used to express the ratio of an amount as a number out of 100. The sign that is used to represent percentage is %.
In order to convert a number to percentage, multiply the number by 100. In order to determine the percent of exams that she has taken, multiply the ratio of exams taken and the total number of exams by 100.
Percent of the exams she has taken = (number of exams taken / total number of exams) x 100
Percent of the exams she has taken = (27 / 36) x 100
Percent of the exams she has taken = 75%
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let f(x)= 2x-9. Find the inverse and evaluate f^1 (-2).
Answer:
f(x)= 2x-9
f(-2)= 2(-2)-9
f(-2)= -4-9
=-13
Ready
Equivalent Expressions & the Distributive Property-
A tiny house has a length of 25 feet. The width of the kitchen is 3 feet, and the width of the
remaining living space is 12 feet.
Which expression represents the area
of the tiny house?
3(12+25)
25-3+12
25(3+12)
3-12 +25
25 ft
3 ft
12 ft
Answer: The area of the tiny house can be represented by multiplying the length of the house by the width. Since the width of the kitchen is 3 feet, and the width of the remaining living space is 12 feet, the total width of the house is 3+12 = 15 feet.
So the area of the tiny house is 25 ft * 15 ft = 2515 = 375 sq ft.
The expression that correctly represents the area of the tiny house is 25 * 15 =375.
So the correct answer is 2515 = 375 ft^2
The other expressions you gave are not the correct representation of the area of the house
3(12+25) = 3 * 37 = 111 ft^2
25-3+12 = 25 - 3 + 12 = 34 ft^2
25(3+12) = 25 * 15 = 375 ft^2
3-12 +25 = 3 - 12 + 25 = 16 ft^2
25 ft , 3 ft and 12 ft are not represent the area of the house.
Step-by-step explanation:
18.
M is the midpoint of WX and
YZ. Is YW = ZX? Why?
W
M
Find the value of x.
Answer:
76 don't know how to explain it
-2(x+5)=4 math homework help
Answer:
-7
Step-by-step explanation:
-2(x+5)=4
First, distributive property,
-2x-10=4
Add 10 to both sides,
-2x=14
Divide both sides by -2
-7
If f(-5)=0, what are all the factors of the function f(x)=x^3-19x+30? Use the remainder Theorem.
The requried other factors of the given function are (x - 2) and (x - 3).
What is the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
here,
Given function, f(x) = x³-19x+30,
One of the factors of function is x = -5 or x + 5 = 0
Following the remainder theorem to determine the others factor,
= given function / one of the factor
= [x³-19x+30] / [x + 5]
= (x - 2)(x - 3)
Thus, the requried other factors of the given function are (x - 2) and (x - 3).
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Please help asap!
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow
Determine P(not orange) if the spinner is spun once.
25%
12.5%
87.5%
37.5%
(no links)
Answer:
7/8 = 87.5%
Step-by-step explanation:
You have only one of eight (1/8) evenly divided sections that is orange. The rest is not orange (1 - 1/8 = 7/8).
Therefore, spinning once will yield 7/8 odds of not landing on orange, or 0.875 or 87.5%.
The probability of not getting orange is 87.5%. The correct option is C.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favourable outcomes to all outcomes.
Probability = Number of favourable outcomes / Number of samples
Given that a spinner with repeated colours numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
You only have one of eight (1/8) evenly divided orange sections.
The rest is not orange,
P = (1 - 1/8
P = 7/8
P = 87.5%
Therefore, spinning once will yield 7/8 odds of not landing on orange or 0.875 or 87.5%.
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renee spent 1/8 of the day landscaping around the house. she spent 1/2 of that time pulling weeds. what fractions of the day did renee spend pulling the weed? PLS HELP IM HAVING A UNIT TEST ON MONDAY
Answer:
Renee spent 1/2 of the time she spent landscaping pulling weeds, which is 1/2 * 1/8 = 1/16 of the day. Therefore, Renee spent 1/16 of the day pulling weeds.
Lupe wrote two different fractions with the same denominator. both fractions were less than 1. can their sum equal? can their sum be greater than 1?
Answer: it depends on the number you took
Step-by-step explanation:
What’s does 1.56x-7.8 equal
Answer:-12.168
Step-by-step explanation: multiply it regularly, then count how many decimals are after the numbers, in this case, 3. cus it’s 2 after 1.56 and one after 7.8
Answer: x=5
Step-by-step explanation:
Solve the rational equation by combining expressions and isolating the variable (x)
Help answer this pls if really appreciate it!! Also if you could explain a little I’d appreciate it extra since I’m a little lost. Thank you!!!
According to the question the angle between right angle triangle hence the M∠1 = [tex]90^{0}[/tex] .
What does a triangle's right angle look like?90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°.
Which three angles make up a right triangle?Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees (they are complementary).
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Find a line that passes through the points (-1,3) and (5,-1)
y2-y1/x2-x1
= (-1-3)/(5+1)
= -4/6
= -2/3
y = -(2/3)x + c
3 = (2/3) + c
c = -2/3 + 3
c = -2/3 + 9/3
c = -7/3
y = (2/3)x + (7/3)