The P(teacher and video games) = 4%; the two events are not independent.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
P(teacher and video games) = number of teachers who play video game / total number of respondents
6/150 = 0.04 = 4%
Independents events are events whose occurrence do not depend on each other. They are random events.
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Answer:
The P(junior and video games) = 32%; the two events are not independent.
Step-by-step explanation:
i got it right aswell
What is the product of (5−6i)(2−3i)
Answer:Multiply using the FOIL method, then combine the real and imaginary parts of the expression.
−
28+3i
Step-by-step explanation:
In a small town in the Himalayas, the average snowfall each month is 6 inches. July is the month with the lowest average snowfall, of 1 inch. Construct a function that models this behavior. During what period is there more than 10 inches of snowfall?
The function that models the above behavior is given as:
f(x) = ACos(B(x + C)) + 6 ..... .......i
where x = 1 (that is January)
D (Average Snowfall) = 6.
Hence, the amplitude (A) is given as:
A = 6-1
= 5
What is a mathematical function?A mathematical function is a function comprising of different variables that represent different factors or events and the relationships between them.
Recall that in a year we have 12 months. Hence, P = 12
→ P = (2π) /.B → (2π)/B = 12 → B = π/6
Taking the values of A and B and plugging them in, we ahve:
F(x) = 5 cos (π/6(x + C)) + 6................ii
This means that in July, we'll have
x = 7 and f(x) = 1
Therefore,
1 = 5cos ((π/6) (7 + C) + 6 → 5 Cos ((π/6) (7 + C) → -5cos ((π/6) (7 + C)
= -1
→ ((π/6) (7 + C) = π
→ 7 + C = 6
→ C = -1
Taking equation ii, we have
F(x) = 5cos ((π6) (x -1)) + 6
F (x) > 10
Therefore
5cos ((π/6) (x-1) + 6 > 10
→ cos ((π/6) (x-1) + 6 > 4/5
→ (π/6) (x-1) > Cos⁻¹ (4/5)
(π/6) (x-1) < 0.6435 and
(π/6) (x-1) > 5.6397
→ x < 2.23 and x > 11.77
The interpretation is that upwards of ten inches of snow fall in January, February, November, and December.
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Select the correct answer from each drop-down menu. Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system? The graph represents the system of inequalities . The test point satisfies both of the inequalities in the system represented by the graph.
The system of inequality that the graph represents is E. 2x + 3y is less than or equal to 4 and 2x + 2y is less than or equal to 3
How to illustrate the graph?In the graph, when 2x + 3y = 4
3y = 4 - 2x
y = -2/3x + 4/3
When 2x + 2y = 3
2y = -2x + 3
y = -x + 3/2
On the graph, -2/3x + 4/3 is illustrated on the first line while -x + 3/2 is illustrated on the second line.
Therefore, the correct option is E.
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Use the Law of Cosines to find the specified missing value. Approximate your answer to the nearest tenth.
If A = 60°, b = 20 ft, c = 30 ft, find B.
Answer:
40.9
Step-by-step explanation:
Law Of Cosines:
[tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}[/tex]
This can generally be understand as the cosine(angle) = the sum of squares of the two other sides - the opposite side squares divided by 2 times the other two sides
If this is to confusing to understand I'll just provide the formula for the other two angles which is essentially the same thing just different variables
[tex]cos(B)=\frac{a^2+c^2-b^2}{2ac}\\\\cos(C)=\frac{a^2+b^2-c^2}{2ab}[/tex]
Anyways for the law of cosines we need all three sides, but since we're given the two other sides, we can also rearrange the equation to solve for the other missing side.
Original Equation
[tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}\\[/tex]
Multiply both sides by 2bc
[tex]cos(A)*2bc=b^2+c^2-a^2[/tex]
Add a^2 to both sides
[tex]cos(A)*2bc+a^2=b^2+c^2[/tex]
Subtract 2bc * cosA from both sides
[tex]a^2=b^2+c^2-2bc*cos(A)[/tex]
So this can be applied for any side, and it can be generally seen as: side ^2 = sum of squares of other two sides - 2 times the other two sides * cos(opposite angle of the original side). If that's to confusing you can also just look at the other formulas which are essentially the same just different variables
[tex]b^2=a^2+c^2-2ac * cos(B)\\c^2=a^2+b^2-2ab*cos(C)[/tex]
anyways, applying this formula we get the equation:
[tex]a^2=20^2+30^2-2(20)(30)*cos(60)[/tex]
Square and multiply values you get
[tex]a^2=400+900-1200*cos(60)[/tex]
Now add the values and you can calculator cos(60) using a calculator or using the unit circle, both should give the same value
[tex]a^2=1300-1200(0.5)[/tex]
Multiply
[tex]a^2=1300-600[/tex]
Simplify
[tex]a^2=700[/tex]
Take the square root of both sides
[tex]a\approx 26.4575[/tex]
So now use this to solve for B using the original law of cosines equation. Plugging in all the sides you get the equation:
[tex]cos(B)=\frac{26.4575^2+30^2-20^2}{2(26.4575)(30)}[/tex]
Square values and simplify denominator
[tex]cos(B)=\frac{700+900-400}{1,587.451}[/tex]
Simplify numerator
[tex]cos(B)=\frac{1200}{1,587.451}[/tex]
Convert to decimal
[tex]cos(B)\approx 0.755[/tex]
Take the inverse cosine of both sides
[tex]B \approx cos^{-1}(0.755)[/tex]
Approximate this using a calculator
[tex]B\approx 40.8934[/tex]
Round to the nearest tenth
[tex]B\approx40.9[/tex]
Ryan has $3$ red lava lamps and $3$ blue lava lamps. He arranges them in a row on a shelf randomly, then turns $3$ random lamps on. What is the probability that the leftmost lamp on the shelf is red, and the leftmost lamp which is turned on is also red
There are 6! = 720 ways of arranging the lamps.
If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.
Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.
Ignoring lamp color for the moment, the probability of arranging 3 lit lamps and 3 unlit lamps is the same, 1/2.
Since Ryan arranges the lamps randomly by color, then turns 3 of them on randomly, the two events are independent. So
P(leftmost red AND leftmost lit) = P(red) × P(lit) = 1/2² = 1/4
NOTE: Angles not necessarily drawn to scale.
Answer:
x = 100 degrees
Step-by-step explanation:
Angle AEG is vertical to angle BEF. Vertical angles are congruent angles. The measure of angle BEF is 100 degrees (80 + 20 = 100), so angle AEG is 100 degrees which makes the measure of x 100 degrees.
The price of a bungalow in 1990 was $850000. If there was a 125% increase in 2000, followed by a 30% decrease in 2013, what was the price in 2013?
Answer:
1,338,750$
Step-by-step explanation:
1990 price was 850,000
in 2000
850,000 + 125% = 1,062,500
850,000 + 1,062,500 = 1,912,500
in 2013
1,912,500 - 30% = 573,750
1,912,500 - 573,750 = 1,338,750
1. If the ratio of AB to BC is 4:9, what is the area of Parallelogram ABCD?
Answer:
not determinable
Step-by-step explanation:
you can't determine--think of it like this: let's say I figure out a combination of two lengths that work, I could always scale it up (or down)
Let's say AB = 4, and BC = 9, then the area would be 36
but let's say AB = 8, and BC = 18, then the area would be 144
so, from this information alone, we cannot find the answer
hope this helps! have a lovely day :)
The area of the given parallelogram is that: It cannot be determined from the information given
How to find the area of the parallelogram?The formula for the area of a parallelogram is:
Area = Base * Height
Now, we are told that the ratio of AB to BC is 4:9.
The most important point here is that we do not know the altitude of the parallelogram; the area of a parallelogram is altitude times base.
A secondary point would be that we do not know the lengths of AB and BC; we only know the ratio of the two sides.
The actual lengths of the sides could be, for example, 8 and 18
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Complete question is:
If the ratio of AB to BC is 4:9, what is the area of Parallelogram ABCD attached?
The line on the graph passes through the points A (0, 6) and B (3, 0).
YA
a) Calculate the gradient of line AB.
b) Find the gradient of a line perpendicular
to AB.
c) Find the equation of the line passing
through point A and perpendicular
to AB.
B
The equation for the line passing through point A and perpendicular to AB will be y-0.5x=6, the gradient of line AB is -2, and the gradient of a line perpendicular to AB is 0.5.
What is the slope or gradient?A numerical assessment of a line's angle relative to the ground is known as the slope.
Given data;
m₁ is the slope of line AB
m₂ is the slope of a line perpendicular to AB
The coordinate points are,
A,(x₁,y₁)= (0, 6)
B,(x₂,y₂)=(3, 0).
The gradient of line AB;
[tex]\rm m_{{1} }= \frac{y_2-y_1}{x_2-x_1} \\\\ \rm m_{{1} }= \frac{0-6}{3-0} \\\\ m_{{1} }=-2[/tex]
The slope of the lines has a perpendicular relation is -1;
m₁ × m₂ = -1
(-2) × m₂ = -1
m₂ = 1/2
m₂ = 0.5
The equation of the line passing through point A and perpendicular to AB;
(y - y₁) = m₂(x-x₁)
(y-6)=0.5(x-0)
y-6 = 0.5 x
y-0.5x=6
Hence, the gradient of line AB, the gradient of a line perpendicular to AB, and the equation of the line passing through point A and perpendicular to AB will be -2,0.5 and y-0.5x=6.
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For the graph, which are possible functions f and g?
The possible functions for f and g are f(x) = [tex]3^{x}[/tex] and g(x) = [tex](\frac{1}{3} )^{x}[/tex]
What is an exponential function?An exponential function is a mathematical function of the following form: f ( x ) = [tex]p^{x}[/tex] where x is a variable, and p is a constant called the base of the function. The most commonly encountered exponential function base is the transcendental number e.
Analysis:
If for every value of x being positive and y is a positive whole number and for every x being negative y is a positive fraction, then that exponential function has a whole number base, Other wise it would have a fractional base. From the above explanation, f has (1,3) (positive x and whole number y) and (-1, 1/3) (negative x and positive fraction y). so therefore f has a whole number base and g has a fraction base.
Therefore f(x) = [tex]3^{x}[/tex] and g(x) = [tex](\frac{1}{3} )^{x}[/tex]
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Can 10 people be divided into two groups with a ratio of 1 : 2? Explain.
No
Let the groups be x and 2x
x+2x=103x=10x=10/3Its decimal not natual so can't be divided
Which expression is equal to the equation?
Answer: [tex]-11\sqrt{7}[/tex]
Step-by-step explanation:
To find the expression equal to the given, we will simplify the original.
Given:
[tex]\displaystyle 2\sqrt{28} -5\sqrt{63}[/tex]
Simplify:
[tex]-11\sqrt{7}[/tex]
Answer: [tex]-11\sqrt{7}[/tex]
Answer: [tex]-11\sqrt{7}[/tex]
Step-by-step explanation:
[tex]2\sqrt{28}-5\sqrt{63}[/tex]
= [tex]2\sqrt{4*7}-5\sqrt{7*9}[/tex]
= [tex]2*\sqrt{4}*\sqrt{7} - 5*\sqrt{7} *\sqrt{9}[/tex]
= [tex]2*2*\sqrt{7} - 5*\sqrt{7}*3[/tex]
= [tex]4\sqrt{7} - 15\sqrt{7}[/tex]
= [tex]-11\sqrt{7}[/tex]
Given a decile cut point value of 10.4, where the tenth sequential value is 32 and the eleventh value is 42, what is the actual decile value
The actual decile value is 126.6
To get the actual decile value, the decile formula is used. The formula used is:
Di = I (n+1) / 10 multiplied by (n - n+1)/10
This implies that the decreased fee, which in this case is 32 + 1, is delivered to the entire multiplication of the cut point 10.4, and the difference among the more tremendous value whilst organized in the ascending fee and the newly brought decreased value.
This gives:
33 + 10.4 * (42 - 33)
= 126.6
The actual decile value is 126.6
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What’s the length of three pipes, when combined they equal 72m, how do I find the answer
Answer:
Each pipe is 24m
Step-by-step explanation:
Given:
three pipescombined equal 72mlet the variable x represent the length of 1 pipeAlgebraic Expression:
3 pipes times length equals 72m (the total length)
3x = 72, we want x to be alone so divided both sides by 3
3x / 3 = 72 / 3
x = 24
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Solve Proportions In the following exercises, solve.
403. A golden retriever weighing 85 pounds has diarrhea. His medicine is prescribed as 1 teaspoon per 5 pounds. How much medicine should he be given?
Answer:
Thus, a golden retriever should be given 19 teaspoon of medicine.
Step-by-step explanation:
Given that a golden retriever weighing 85 pounds has diarrhea. His medicine is prescribed as 1 teaspoon per 5 pounds.To find how much medicine should he be given.Assign a variable. Write a sentence that gives the information to find it.Translate into a proportion be careful of the units.Multiply both sides by the Least Common Denominator and simplify. Check the answer.Step 1 of 3
Write the data in mathematical form and simplify.
Let x=the number of teaspoon
If 1 teaspoon medicine is 5 pounds then 85 pounds is how many teaspoon of medicine.
Translate the statement into proportion.
[tex]\begin{aligned}\frac{\text { pounds }}{\text { teaspoon }} &=\frac{\text { pounds }}{\text { teaspoon }} \\\frac{5}{1} &=\frac{85}{x}\end{aligned}[/tex]
Step 2 of 3
Multiply both sides by x and simplify
[tex]$x(5)=\frac{85}{\bcancel{x}}(\bcancel{x})[/tex]
5x=85
Divide by 5,
[tex]x=\frac{85}{5}[/tex]
Simplify, x=19
Step 3 of 3
Check the answer.
Substitute x=19 in original proportion and simplify.
[tex]$$\begin{aligned}\frac{5}{1} &=\frac{85}{x} \\5 &=\frac{85}{19}\end{aligned}$\\ \\ Hence, $5=5$, True[/tex]
Leonard has built a crate for his car. The crate measures (x+5) ft by (x+1) fr by (2x+3) ft. Write an expression that represents the volume in the crate in cubic feet
Answer:
(x+5)(x+1)(2x+3) cubic feet
Step-by-step explanation:
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4 (x-8). What
IS the slope-intercept form of the equation for this line?
O y= 1/4x -12
O y= 1/4x-4
O y=1/4x+2
O y= 1/4x+6
Answer:
y = (1/4)x + 2
Step-by-step explanation:
y - 4 = 1/4 (x-8)
y - 4 = 1/4(x) - 2
y = (1/4)x + 2
16 The perimeter of the pentagon is equal to the perimeter of the square.
Not to scale
5X tỉ 3
2x + 3
11
7x + 4
5x + 8
9x10
Find an expression for the length of one side of the square.
Give your answer in terms of x in its simplest form.
7x+2
Step-by-step explanation:
add all the sides of the pentagon and make it equal to the perimeter of the square which is 4y
sides of the pentagon are
5x+3
2x+3
7x+4
9x-10
5x+8
28x+8=4y
7x+2 = y
7x+2 = answer
gathmath
gathmathier6961
another way :
in a standardized test you may want to use real numbers
make x equal a prime number like 3
so then the sides are
18
9
25
17
23
=
92
then divide by 4
23
then divide by 3
which is 7 remainder of 2
which is
7x+2
9-5(x+4) = 3(2-x) - 1
Answer: x=-8
Step-by-step explanation:
Question 2 of 5
Drag each tile to the correct box. Not all tiles will be used.
A scientist conducted an experiment to determine how effective an organic cleaner is at killing bacteria. To conduct the experiment, the
scientist randomly selected 50 doorknobs in an office building. She cleaned 25 of the doorknobs with the organic cleaner
(subject group 1). She did not clean the remaining 25 doorknobs (subject group 2).
After applying the treatments to each group, the scientist tested each doorknob to measure bacterial growth.
Which description matches each term?
bacterial growth
subject group 2
the scientist
water
control group
explanatory variable
response variable
subject group 1
Submit
-C
organic cleaner
Reset
Thanks y’all for helping :)
Based on the terms given on the population type and the variables, the correct matches are:
Population - all 108 restaurant locations in the chain. Frame - the list of all restaurant locations in the chain. Sample - the 10 randomly selected locations. Control group - subject group 2.explanatory variable - organic cleaner.response variable - bacterial growth.What are some terms in research?The population is total set of items that a sample is drawn from and in this case it all the restaurants. The sample would be the selected items from the population.
The control group is the group that is not manipulated by the explanatory variable which is the organic cleaner. The response variable is what changes as a result of the explanatory variable so it is bacterial growth.
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Find the value of x. Round to the
nearest tenth.
9
4
X =
Step-by-step explanation:
ATTACHED IS THE SOLUTION!A department store placed 144 suits on sale. By
the end of the day 108 suits had been sold. What
percent of the suits were sold on the day?
Answer:
75%
Step-by-step explanation:
[tex]\frac{108 }{144} = 0.75[/tex]
0.75 * 100 = 75%
Find the equation of the horizontal line at a height of -3.9.
y = -3.9x
x = -3.9
y = -3.9
the height must be an integer
The equation of the line will be y = -3.9, and the height after rounding off will be -4.
What is a straight line?
A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The horizontal line can be defined as:
y = a
Where a is the constant.
Here a = -3.9
y = -3.9
The height = -3.9 ≈ -4
Thus, the equation of the line will be y = -3.9, and the height after rounding off will be -4.
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pls help - Which number is the additive inverse of –5?
– One-fifth
0
Negative one-fifth
5
Answer:
5
Step-by-step explanation:
a number and its additive inverse sum to zero , then
the additive inverse is the opposite of the number
the opposite of - 5 is + 5
and - 5 + 5 = 0
Find the value of x. please helpp
Answer:
A
Step-by-step explanation:
given 2 secants drawn from an external point to the circle , then
the product of the measures of one secant's external part and that entire secant is equal to the product of the other secant's external part and that entire secant, that is
9(9 + 2 + 3x) = 10(10 + 2x + 2)
9(11 + 3x) = 10(12 + 2x) ← distribute parenthesis on both sides
99 + 27x = 120 + 20x ( subtract 20x from both sides )
99 + 7x = 120 ( subtract 99 from both sides )
7x = 21 ( divide both sides by 7 )
x = 3
Answer:
(A). 3
Step-by-step explanation:
[ 9 + ( 2 + 3x )] × 9 = [ 10 + ( 2x + 2 )] × 10
27x + 99 = 20x + 120
7x = 21
x = 3
Find y. Help me please thank u:)
The value of y is 116 degrees
How to solve for y?To solve for y, we make use of the following angle theorem.
The angle at the center is twice the angle at the circumference.
So, we have:
y = 2 * 58
Evaluate the product
y = 116
Hence, the value of y is 116 degrees
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Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solutions. (2 points) Equation 1 Equation 2 |5x + 6| = 41 |2x + 13| = 28 Equation 1 has more solutions than equation 2. Equation 1 and Equation 2 have the same number of solutions. Equation 2 has more solutions than Equation 1. The number of solutions cannot be determined.
Answer:
Step-by-step explanation
5+5
helpppp!!!!!!!!!!!!!
Answer:
D is the right answer.
Perimeter is the distance around an objectArea represents space inside a 2-D objectVolume represents space inside a 3-D objectHope it helps!
Rectangle A and Rectangle B are similar. Rectangle A has side lengths of 20 and 15. Rectangle B has a side length of 60. What are the possible values for the length of the other side of Rectangle B? Select all that apply.
- 40
- 45
- 80
- 100
what’s the answer to this?
The solution set of the compound inequality is (-∞, 9] ∪ [17, ∞) and the correct graphical representation on the number line can be seen in the first option.
What is a solution set of a compound inequality?The solution set of a compound inequality is the set of values that intersect between the two inequalities and they satisfy the solution to each individual inequality.
The graph of a compound inequality can be illustrated on the number line.
From the given information, we have:
[tex]\mathbf{-\dfrac{1}{3}x+10 \geq 7}[/tex]---- (1)
x - 10 ≥ 7 ----- (2)
From equation (1), the solution to the inequality is:
x ≤ 9 and the interval notation can be represented as (-∞, 9]The solution to the second inequality is:
x ≥ 17 and the interval notation is [17, ∞)The solution set of the compound inequality is (-∞, 9] ∪ [17, ∞) and the correct graphical representation on the number line can be seen in the first option.
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