if an organization wants to test whether a minority of its employees are dissatisfied with their bonuses, the null hypothesis would be that the true population proportion would be equal to 0.5
This is further explained below.
What is the null hypothesis?Generally, The null hypothesis is a common kind of statistical theory that proposes there is no statistical link and significance between two sets of observed data and measurable phenomena in a set of provided single observable variables.
In conclusion, In the event that a company is interested in determining whether or not a subset of its workers are unsatisfied with the incentives they get, the null hypothesis would state that the actual population percentage would be equal to fifty percent.
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CQ
If an organization wants to test whether a minority of its employees are dissatisfied with their bonuses, the nult hypothesis would be that the true population proportion would be: less than 5 OOOO greater than 5 not equal to 5 .5
fifteen dots are evenly spaced on the circumference of a circle. how many combinations of three dots can we pick from these 15 that do not form an equilateral triangle?
There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.
Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.
Here, we will use the combination rule to find out the possible triangles,Thus, the total number of possible triangles = 15C3 = (15.14.13) / (1.2.3) = 455
Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.
For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.
And 12/3 = 4 dots would be between any two connecting dots.
Taking 1st connecting dot, the second connecting dot would be
1 + 4 + 1 = 6th
Similarly, the third connecting dot would be 6 + 4 + 1 = 11th
So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);
After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:
So, there are 455 - 5 = 450 triangles that are not equilateral triangles.
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olve for? (Part 1)
Cool Down: A Rectangular Relationship
The perimeter of a rectangle is 48 centimeters. The relationship between the length, the
width, and the perimeter of the rectangle can be described with the
equation 2 length + 2 width = 48.
Find the length, in centimeters, if the width is:
1. 10 centimeters
2.3.6 centimeters
3. w centimeters
Question 1
[tex]2l+2w=48 \\ \\ 2l+20=48 \\ \\ 2l=28 \\ \\ l=14\text{ cm}[/tex]
Question 2
[tex]2l+7.2=48 \\ \\ 2l=40.8 \\ \\ l=20.4 \text{ cm}[/tex]
Question 3
[tex]2l+2w=48 \\ \\ l+w=24 \\ \\ w=24-l[/tex]
How do you write 3.5 as a percentage? Write your answer using a percent sign (%).
Answer:
350%
Step-by-step explanation:
1) To convert a decimal to a percentage multiply the given decimal by 100. So,
3.5 x 100 = 350
2) 350% is the final answer
Make x the subject of m = n+x/p
When x is made the subject of m= n+ x/p,
x = mp - n
How is x made the subject of m = n +x/p ?
[tex]m = \frac{n+x}{p} \\\\mp = n+x\\\\mp -n = x\\\\x = mp-n[/tex]
How is x being made the subject?
To make x the subject of the formula or equation, the formula or equation must be rearranged so that we have a single x variable that is equivalent to the other variables in the formula.After rearranging the equation, each term containing x should be put on the same side of the equation.Just one x needs to be displayed at the conclusion to make it the subject.If x occurs in several terms, factorization might be necessary.The result of square rooting a number or variable as an inverse operation may be positive or negative.To learn more about making x the subject, refer:
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brainly to whoever answers first!!
MODELING REAL LIFE You make a total of
11 one-point free throws, two-point shots, and
three-point shots in a basketball game and score a
total of 22 points. You make two more two-point
shots than three-point shots. How many of each
type of shot do you make?
Stat 0,-10 and -6,-8
The midpoint of the given coordinates of points (0,-10) and (-6,-8) is ( -3,-9 )
How determine the midpoint between two point?A midpoint is simply a point that divides a line segment into two equal halves.
The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point 1( 0,-10 )
x₁ = 0y₁ = -10Point 2( -6,-8 )
x₂ = -6y₂ = -8Midpoint = ?
To determine the midpoint, plug the given points into the midpoint formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( ( 0 + (-6) )/2, ( (-10) + (-8) )/2 )
M = ( ( 0 - 6) )/2, ( -10 - 8 )/2 )
M = ( ( -6 )/2, (-18 )/2 )
Midpoint M = ( -3,-9 )
Therefore, the midpoint of the coordinates is ( -3,-9 ).
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EVENING PUZZLE: 7 years ago I was 7 years older, 7years Later how old am I?
Answer:
21
Step-by-step explanation:
You are 14 right now if you were 7 yo 7 years ago. Add 7 more years to 14 and you get 21
Decrease £47 by 24%
Give your answer in pounds (£).
The most appropriate choice of percentage will be given by-
£47 after 24% decrease becomes £35.72
What is Percentage?
Percentage is a ratio expressed as a percentage of 100.
Here,
Original Price = £47
Percentage decrease = 24 %
Decrease in Price = £([tex]\frac{24}{100} \times 47\\[/tex])
= £11.28
New Price = £(47 - 11.28)
= £35.72
So, £47 after 24% decrease becomes £35.72
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a collection of 65 coins contains one with two heads. the remainder of the coins are fair. if a coin, selected randomly from the collection, turns up heads 6 times in 6 tosses, what is the probability it’s a two-headed coin?
a collection of 65 coins contains one with two heads. the remainder of the coins are fair. if a coin, selected randomly from the collection, turns up heads 6 times in 6 tosses, 1/65 is the probability it’s a two-headed coin
Definition of probability
(1) : the chance that a given event will occur. (2) : the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
We know that one coin in a collection of 65 has two heads. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row. We calculate the probability that it is the two-headed coin.
We calculate the number of possible combinations:
C₁⁶⁵= 65!/1!(65-1)!
= 65
Number of favorable combinations is 1.
Therefore, the probability is
P=1/65.
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In a scale drawing, a rectangle has a length of 6.1 inches. The actual rectangle has a length of 85.4 inches.
Using proportions, it is found that the scale of the rectangle is of 1:14.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division to find the unit rates.
One example of application of proportions is for scale problems, as the scale is given by the following equation:
Scale = Drawn distance : Actual distance.
For this problem, we have that:
The drawn distance is of 6.1 inches.The actual distance is of 85.4 inches.Hence the scale is of:
6.1 : 85.4.
We can simplify dividing 85.4 by 6.1, hence:
85.4/6.1 = 14.
Hence the simplified scale is:
1:14.
What is the missing information?This problem is incomplete and could not be found on any search engine, hence we are going to suppose that it asks for the scale of the drawing of the rectangle.
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6. a. i. Using a scale of 2cm to 2units on both axes, draw on a sheet of graph paper two axes ox and 0 to 10 ii. On this graph sheet, mark the x-axis from 10 to 10 and the yaxis from -10 to iii. Draw triangle PQR with coordinates, P(2,2) Q(4,6) and R(6,2). iv. Draw the image triangle PQ,R of triangle PQR under a refection in the line 0 where P→ P₁, QQ, and RR, Write the coordinates of P₁, Q, and R. v. The image triangle P, Q, R, of triangle P₁, Q₁, R, under a rotation of 180° about the origin when P,→P₂, Q₁→Q₂ and R,→R₂. Write down the coordinates of P₁ Q₂ R₂. vi. Find P,R..
Answer:
i dunno
Step-by-step explanation:
hard man
What is the value of −4 + (−16) + 23?
43
3
−11
−35
Step-by-step explanation:
3 ................
.
........................
Answer:
3
Step-by-step explanation:
–4 + (–16) + 23
–4 – 16 + 23
–20 + 23
= 3
What is the value of x?
(2x - 5)°
n
l
m 45°
Answer:
x = 70
Step-by-step explanation:
(2x - 5) and 45 are same- side interior angles and sum to 180° , that is
2x - 5 + 45 = 180
2x + 40 = 180 ( subtract 40 from both sides )
2x = 140 ( divide both sides by 2 )
x = 70
Please help me with this question!! :)
Answer:
D. The last 26/8, 3-32, -Pi, -4 2/3
Step-by-step explanation:
26/8= 3.25
3-32=3.17
-Pi= -3.14
-4 2/3= -4.67
A snowboarder leaves an 8-foot-tall ramp with an upward velocity of 28 feet per second. The function h=16t+28t+8 gives the height h (in feet) of the snowboarder after t seconds. What is the maximum height of the snowboarder?
The maximum height of the skateboarder is 40.25 feet after 0.875 seconds
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let h(t) represent the height of the skateboarder after t seconds.
h(t) = -16t² + 28t + 8
The maximum height is at h'(t) = 0
h'(t) = -32t + 28
-32t + 28 = 0
32t = 28
t = 0.875s
h(0.875) = -16(0.875)² + 28(0.875) + 8 = 40.25 feet
Maximum height is 40.25 feet
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find the value of g(ƒ(1))
f(x) = −2x +4
g(x) = 3x² - 7x +9
Answer:
f=4
Step-by-step explanation:
I think it's right but not 100% sure
The function fis defined by the following rule.
f(x) = 5x-2
Complete the function table.
Description of a Function : Consider two nonempty sets, X and Y. A relation that links exactly one element from X to Y is known as a function from X into Y.
f(x) = 5x-2 ?
Solution:
f(x) = 5x-2
5x-2 = 0
5x = 2
x = 0.4
f(0.4) = 5(0.4)-2
= 0
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The normal price of a computer game is £40
The price is reduced by 1/5 in a sale.
Work out the price of the computer game in the sale.
Answer:
£32
Explanation:
so 1/5 = 0.2
to make 0.2 a percent just multiply by 100 so 0.2 • 100 = 20%
so the discount would be 20%, meaning the game holds 80% of its value since
100-20 = 80
so to make 80% a decimal, divide by 100 so 80/100 = 0.8
so then you just multiply: 40 • 0.8 = 32
so the game is £32
hope this helps :)
The price of the computer game on sale is £32.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, The normal price of a computer game is £40.
The price is reduced by 1/5 in a sale.
∴ The price of the computer game on discount can be obtained if we subtract the fraction of the discount times the normal price from the normal price which is,
= {(40 - (1/5)×40}.
= {40 - 8}.
= £32.
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My truck loses 3 gallons of gas for every mile. What integer represents the change in gas after 7 miles
Answer:
21
Step-by-step explanation:
If it loses 3 gallons every mile, then multiply it by 7.
3*7 = 21
Another way to solve this is by using linear equations
y=3x
replace x with 7 and y would be equal to 21
Your friend
writes the word sentence as an inequality. Is
your friend correct? Explain your reasoning.
Twice a number x is at most-24.
2xS-24
Answer:
Yes, the friend is correct.
Step-by-step explanation:
Twice a number of x is the same as saying multiply x by 2, which equals 2x. At most means 2x can only reach -24 at the very max, so solving for x will give you an answer that should only either be less than or equal to -24. This equation is an inequality because an inequality compares two values; in this case, the inequality is comparing 2x is at most -24, which is the same as saying 2x is less than or equal to -24.
7) A plane which can fly 550 mph in still air flies for 3 hours against a wind and for 2 hours with the
same wind. The total distance it covers is 2725 miles. Find the rate of the wind.
Answer:
25 mph
Hope this helps! :)
Analyze the biconditional statement below and complete the instructions that follow.
A polygon is a hexagon if and only if it has six sides.
Write a definition based on the given biconditional.
A.
A polygon has six sides if and only if it is a hexagon.
B.
A polygon is a hexagon with six sides.
C.
A hexagon is a polygon with six sides.
D.
If a polygon is a hexagon, then it has six sides.
The definition based on the given biconditional is B. A polygon is a hexagon with six sides.
What is a biconditional statement?A conditional statement combined with its opposite is known as a biconditional statement. As a result, one conditional is only true if and when the other is also true. It frequently employs the phrase "if and only if" or the abbreviation "if." It serves as a reminder that the conditional must be true in both directions by using the double arrow.
The biconditional statement is that the polygon is a hexagon if and only if it has six sides.
Therefore, the correct option that illustrates this is B.
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SA=2\pi r^{2}+2\pi rh[/tex]
use 3.14 for [tex]\pi[/tex]
Find the surface area of a water tower that is 40 feet tall and has a diameter of 30 feet.
DO NOT ROUND YOUR ANSWER.
Thee surface area of the water tower is 1664 square feet
How to determine the surface area
It is important to note that the formula for determining the surface area of a cylinder is expressed as;
Surface area = 2πr² + 2πrh
Where;
The value for pi = 3.14The height of the water tower is 40 feetThe diameter of the water tower is 30 feetAlso, note that the formula for diameter is expressed as;
Diameter = 2r
Substitute the value of diameter
30 = 2r
r = 15 feet
Now, substitute the values into the formula
Surface area = 2(3.14)(15)² + 2(3.14)(40)
expand the bracket
Surface area = 1413 + 251. 2
Add the values
Surface area = 1664. 2
Surface area = 1664 square feet
Hence, the value is 1664 square feet
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2.5 m³ of marble has a mass of 6775 kg.
3
a) Calculate the density of marble in kg/m³.
b) Find the mass of 1.9 m³ of marble in kg.
Answers:
a) 2710 kg/m³
b) 5149 kg
====================================================
Work shown for part a)
density = mass/volume
density = (6775 kg)/(2.5 m³)
density = (6775/2.5) kg/m³
density = 2710 kg/m³
-----------------------------------
Work shown for part b)
density = mass/volume
mass = density * volume
mass = (2710 kg/m³) * (1.9 m³)
mass = (2710*1.9) kg
mass = 5149 kg
Line r is shown in the xy-plane. Line q (not shown) is perpendicular to line r. What is the slope of line q?
The Slope of the line q equals 3.
Given the slope of line r is -
slope = perpendicular / base
Finding the equation of line using coordinates (2,3) and (-1,4)
putting the values in the equation,
y2 - y1 / x2 - x1
⇒ 4-3 / -1 -2
⇒ 1/-3
⇒ -1/3
Slope of the line r is -1/3
As line q is perpendicular to line r,
Using the property, 2 lines perpendicular to each other have slope = negative reciprocal of slope 1
the slope of line q becomes 3
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omg for the 3rd time PLEASE I NEED HELP :(
the sides of a right-angled triangle are related like 3 : 7 and the height drawn on the hypotenuse is 42cm. calculate the projections of the sides on the hypotenuse
The 3 : 7 ratio of the leg lengths and the 42 cm length of the hypotenuse side using Pythagorean theorem, gives the lengths of the sides (the legs of the right triangle) as follows;
[tex]147 \cdot \sqrt{ \frac{2}{29} } [/tex] and [tex] 63 \cdot \sqrt{ \frac{2}{29} }[/tex]
What is Pythagorean theorem?Pythagorean theorem states the square that has the hypotenuse of a right triangle as its side length is equal in area to the sum of the areas of the two squares formed by legs of the right triangle.
Given;
The possible given parameters are;
The ratio of the length of the sides (the legs) of the triangle is 3 : 7
The length of the hypotenuse side = 42 cm
Required: The lengths of the other two sides of the triangle
Solution;
The lengths of the two sides are found as follows;
Let a and b represent the lengths of the legs of the right triangle, according to Pythagorean theorem, we have;
a² + b² = 42²
The ratio of the leg lengths gives;
a/b = 3/7
Therefore;
a = (3/7)•b
Which gives;
((3/7)•b)² + b² = 42²
b²•((3/7)² + 1) = 42²
b = 42²/(((3/7)² + 1)) = 42²×(58/49)
[tex]b = 147 \cdot \sqrt{ \frac{2}{29} } [/tex]
Which gives;
[tex]a =\frac{3}{7} \times 147 \cdot \sqrt{ \frac{2}{29} }= 63 \cdot \sqrt{ \frac{2}{29} }[/tex]
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Which expression is the completely factored form of y² + 2y - 15
O (y-5)(y+3)
O (y+5)(y+3)
○ (y+5)(y-3).
O(y-5)(y-3)
Answer:
(y+5)(y-3)
Step-by-step explanation:
..........
Answer:
y^2-3y+5y-15
y(y-3)+5(y-3)
(y-3) (y+5)
If a company's current sales revenue is $1,386,000 and its marketing objective is to increase sales by 10 percent during the next year, what is the dollar sales goal or the following year?
Answer: ales revenue = 1,386,000 dollars Increase sales in percent = 10 percent Increase sales in dollars = 1,386,000 dollars * 0,1 = 138,600 dollars New sales goal in dollars = 1,386,000 dollars + 138,600 dollars = 1,524,600 dollars
New sales goal is 1,524,600 dollars.
Step-by-step explanation:
solve using completing the square.
[tex] {x}^{2} + 2x - 15 = 0[/tex]
[tex]x^{2} + 2x - 15 = 0[/tex] -> [tex](x+1)^{2} - 16 = 0[/tex]
-> [tex](x+1)^{2} = 16[/tex]
-> x+ 1 = 4 or -4
-> x = 3 or -5
Answer:
[tex]x=3, \quad x=-5[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]x^2+2x-15=0[/tex]
Solve by Completing the SquareStep 1
Move the constant to the right side of the equation:
[tex]\implies x^2+2x-15+15=0+15[/tex]
[tex]\implies x^2+2x=15[/tex]
Step 2
Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:
[tex]\implies x^2+2x+\left(\dfrac{2}{2}\right)^2=15+\left(\dfrac{2}{2}\right)^2[/tex]
[tex]\implies x^2+2x+1=15+1[/tex]
[tex]\implies x^2+2x+1=16[/tex]
Step 3
Factor the perfect square trinomial on the left side:
[tex]\implies (x+1)^2=16[/tex]
Step 4
Square root both sides:
[tex]\implies \sqrt{(x+1)^2}=\sqrt{16}[/tex]
[tex]\implies x+1=\pm4[/tex]
Step 5
Subtract 1 from both sides:
[tex]\implies x+1-1=-1\pm4[/tex]
[tex]\implies x=-1\pm4[/tex]
Solutions
[tex]\implies x=-1+4=3[/tex]
[tex]\implies x=-1-4=-5[/tex]
Therefore, the solutions of the given quadratic equation are:
[tex]x=3, \quad x=-5[/tex]
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