The probability for Jacie or Robyn would consume cheese on a random day is 0.15.
What is defined as the independent events?Two occurrences are considered independent if indeed the occurrence of one does not alter the likelihood of the occurrence of the other. The mathematical expression of event independence A and B is the chance of both A and B occurring being equal to the sum of both the probabilities of both B and A (i.e., P) (A and B).The likelihood of Jacie eating cheese on any particular day is 0.6.
The likelihood of Robyn eating cheese on any particular day is 0.25.
Both events are independent.
As a result, the probability for Jacie or Robyn would consume cheese on a random day is;
P(Jacie or Robyn) = P(Jacie). P(Robyn)
P(Jacie or Robyn) = 0.6 x 0.25
P(Jacie or Robyn) = 0.15
Thus, the probability for Jacie or Robyn would consume cheese on a random day is 0.15.
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what is the measure of EAC?
The measure of angle EAC IS 50°
What is an angle bisector?The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.
∠BAE = x + 30, ∠EAC = 3x - 10
If AE is a line that bisects BAC,
then ∠BAE = ∠EAC
which becomes,
x + 30 = 3x - 10
collecting like terms,
x - 3x = -10 - 30
-2x = -40
x = -40/-2
x = 20°
But m ∠EAC = 3x - 10
substituting x = 20°
we have ∠EAC = 3(20) - 10
= 60 - 10
∠EAC = 50°
In conclusion, the value of ∠EAC = 50°
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13.ERROR ANALYSIS Describe and correct the error in
the student's reasoning.
Answer:
Step-by-step explanation:
3. Martin finishes a swim race in 78.934 seconds. His teammate, Abby finishes the race in 83.978 seconds and their last teammate finishes the race in 84.765 seconds.
CHALLENGE: How many minutes in total did they spend completing the race?
Help me pkleasee :((
The number of minutes in total that the three swimmers spent in completing the race is; 4.12795 minutes
How to carry out units conversion?We are given;
Time taken by Martin to finish swimming = 78.934 seconds
Time taken by Abby to finish swimming = 83.978 seconds
Time taken by the last teammate to finish the race = 84.765 seconds
Thus;
Total time taken by the three swimmers to finish the race = 78.934 + 83.978 + 84.765 = 247.677 seconds
Now, we want to know the total time they spent in minutes and we know that the unit of conversion is;
60 seconds = 1 minute
Thus;
247.677 seconds = (247.677 * 1)/60 = 4.12795 minutes
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Give the numerical coefficient of the term.
−7x
The numerical coefficient is _____.
The numerical coefficient is -7
How to determine the numerical coefficient?From the question, the expression is given as
-7x
Considering an expression given as
Ax
The numerical coefficient of the above expression is A
When compared to the expression -7x, we have
The numerical coefficient is -7
So, we can conclude that the numerical coefficient of -7x is -7
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Answer:
-7
Step-by-step explanation:
The numerical coefficient is -7
an isosceles triangle has a base that measures x 2 with legs that measure 4x - 3 and 2x 5. what is the value of x? an isosceles triangle has a base that measures x 2 with legs that measure 4x - 3 and 2x 5. what is the value of x?
The value of x is 4 for the isosceles triangle has a base that measures x+2 with legs that measure 4x-3 and 2x+5.
What is an isosceles triangle?Therefore, an isosceles triangle has two equal sides as well as two equal angles. An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal. The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.
Here,
Since the adjacent sides of isosceles triangles are equal,
4x-3=2x+5
4x-2x=5+3
2x=8
x=4
The isosceles triangle has a base that measures x+2 and legs that measure 4x-3 and 2x+5, so x is equal to 4.
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express (3) - (2tan^2 x) in terms of cos x
The expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. Similarly, any tirigonometric equation can be convereted into other forms of trigonometric functions.
What is trigonometric functions?
Denoting the relation between a right-angled triangle's angle and sides are trigonometric functions, which are periodic functions.
Consider the given expression.
[tex]3-2tan^2x\\[/tex]
Now, substitute [tex]\frac{sinx}{cosx}[/tex] for [tex]tanx[/tex] as follows:
[tex]3-2tan^2x=3-2(\frac{sinx}{cosx})^2\\=3-2(\frac{sin^2x}{cos^2x})[/tex]
Now, all the terms are converted into cos x except the sin x terms in the numerator. Hence, using the relation between sin x and cos x. Substitute [tex]1-cos^2x[/tex] for [tex]sin^2x[/tex].
[tex]3-2tan^2x=3-2(\frac{1-cos^2x}{cos^2x})[/tex]
Now, all the terms are in cos x. Hence, the expression of [tex]3-2tan^2x\\[/tex] in terms of [tex]cosx[/tex] is [tex]3-2(\frac{1-cos^2x}{cos^2x})[/tex]. In the similar way any function can be conveted into other trigonometric functions.
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Complete the function table. Function: t = 5d − 2
The table for the linear equation is summarized below:
d t
3 13
4 18
5 23
6 28
How to complete a table related to a linear function
In this problem we have a two-column table associated to a linear function, the first column of the table represent a set of values of the domain (d) of the function and the second column of the table is for the set of values of the range (t) of the same. We need to fill the second column of the table with the values associated with the range:
d = 3
t = 5 · 3 - 2
t = 15 - 2
t = 13
d = 4
t = 5 · 4 - 2
t = 20 - 2
t = 18
d = 5
t = 5 · 5 - 2
t = 25 - 2
t = 23
d = 6
t = 5 · 6 - 2
t = 30 - 2
t = 28
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The table below shows the energy of a 10 kg ball as a function of velocity. How much energy will the ball have at 10 m/s? velocity 0,2,3,6,10 energy 0,20,45,180,?
The amount of energy that the ball will have at 10 m/s is; 600 J
How to find the energy from velocity?From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.
If we take the square of the velocity, we get 2² = 4.
Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.
Similarly;
For velocity equal to 3 m/s, the energy is given as:
E = 6 * 3²
E = 54 J
Thus, the general formula to find the energy is given as:
E = 6 * v²
where;
E is the energy
v is the velocity
Now, for velocity equal to 10 m/s, energy is given as;
E = 6 * 10
E = 60 J
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125.8% of £188.83
Give your answer rounded to 2 DP.
The answer is 237.55
Define Percentage
A ratio or figure stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
Given expression is,
125.8% of £188.83
Rewrite it as,
⇒ 125.8 / 100 * 188.83
⇒ 1.258 * 188.83
⇒ 237.54814
⇒ 237.55 (rounded to 2 Decimal places)
Hence, the answer is 237.55
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HELPP!!!1 i'm rushing like i need to summit that ASAP!!
The missing expression in step 2 should be [(6² + 2)/0.5] - 14.8 ÷ 8.
The missing expression in step 6 should be 76 - 1.85.
How to evaluate and solve the given expression?In order to evaluate this expression, we would apply the PEMDAS rule, where mathematical operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
For step 1, we have the following:
[(6² + 2)/|-0.5|] - 14.8 ÷ 8.
In step 2, we would take the absolute value of -0.5:
[(6² + 2)/0.5] - 14.8 ÷ 8.
Therefore, we would have the quantity of the sum of six squared (6²) plus two (2) divided by 0.25, minus 14.8 ÷ 8
In step 3, we would take the exponent of 6:
[(36 + 2)/0.5] - 14.8 ÷ 8.
In step 4, we would add 36 and 2 together:
[(38)/0.5] - 14.8 ÷ 8.
In step 5, we would divide 38 by 0.5:
76 - 14.8 ÷ 8.
In step 6, we would divide 14.8 by 0.5:
76 - 1.85
In step 7, we would subtract 1.85 from 76 as follows:
Solution = 76 - 1.85 = 74.15.
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If f(x)=4x^3+5, then what is the remainder when f(x) is divided by x−3?
Using Remainder theorem
Answer:
113
Step-by-step explanation:
Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.
f(x) = 4x^3 + 5
f(3) = 4(3)^3 + 5
f(3) = 4(27) + 5
= 108 + 5
= 113
See image.
Write and graph linear equations
The equation of linear equation is y = -5x +3.
What is equation of linear equation?
A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.
The slope intercept form of linear equation is
y = mx + b
where m is the slope.
Given,
The slope = -5
and the points are (4, -17)
y = -17, x = 4, m = -5
-17 = -5(4) + b
-17 = -20 + b
-17 + 20 = b
b =3
The equation of linear equation is y = -5x + b
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Solve the system of equations.
Answer:
(7,5)
Step-by-step explanation:
[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]
Solve for x:
[tex]\sqrt{x-3} =\sqrt{x} +3[/tex]
A. -2
B. 2
C. no solution
D. 4
Answer: The answer is C: No solution
Step-by-step explanation:
By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]
You then cancel out the equal terms, in this case x, to reach the equation:
[tex]-3=6\sqrt{x} +9[/tex]
This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.
Write
y − 2 = (x + 6) in
standard form.
ERROR ANALYSIS Describe and correct the error. QRS=VWX by the ASA Congruence Theorem
Answer:
The error made is that the ASA theorem cannot be used here because the congruent side is not directly in between the two congruent angles in either triangle. Really, the information we are given is Angle-Side-Side, not Angle-Side-Angle, and this is not a congruence theorem unless the triangles given are right triangles.
1. A typical Chinese restaurant will often feature a Special Dinner, in which the customer has the choice of ordering one appetizer and one entree.
a. If there are 8 appetizers and 11 entrees, how many different Special Dinners
are there?
b. If there are 12 appetizers and 7 entrees, how many different Special Dinners
are there?
a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
Given that,
In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.
We have to find
a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.
b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.
We solve
a) We just multiply
8×11=88
b) 12×7=84
Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
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The area of rectangle abcd is 28 cm a) what is the length of side ab in terms of x? length of ab = 4 cm x cm 6 cm x cm b) if the area of rectangle abcd is 28 cm?, we can show that x2 + ax = b where a and b are integer values. work out the values of a and b. a : (1) b= (1) total marks: 3
The length AB of rectangle in terms of x is (4 + x) and values of a and b are 10 and 4.
The side AB measures (4 + x). Hence, the length of AB in terms of x is (4 + x).
The area of rectangle is calculated by the formula-
Area = length × breadth
Keep the values in formula -
28 = (4 + x) (6 + x)
Performing multiplication of both brackets with each other
28 = 24 + 4x + 6x + x²
Solving and rewriting the equation
x² + 10x = 4
Equation in question - x² + ax = b
Comparing both the equations, we get a = 10 and b = 4.
Thus, length of AB is (4 + x) and value fo a is 10 and b is 4.
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Which step contains a mistake in solving for the system of equations?
x + 2y = 5
y = 3x - 8
1. x + 2(3x) - 8 = 5
2. x + 6x - 8 = 5
3. 7x = 13
4. x = 13/7
5. 7x 8 5
Answer:
First step, correct answer is (3,1)
Step-by-step explanation:
1.it should be x+2(3x-8)=5
2. x+6x-16=5
3.7x=21
4. 7x/7=21/7
5. x=3
then you can eitheir take x+2y=5 or y=3x-8 i suggets taking second option as it is easier, just input values for x in
) 3x-8=y
6. 3(3)-8= 1
7. x=3, y=1
3. Functions f and g are shown below. Which
best represents
function g?
a. g(x) = f(x) - 3
b. g(x) = -f(x)
c. g(x) = f(x)
d. g(x) = f(x - 2)
Answer:
i think it might be c
Step-by-step explanation:
one class period at lily's school lasts for an hour and fifteen minutes, or $\frac{5}{4}$ hours. however, her biology class usually spends the first five minutes of that time talking and the next ten minutes reviewing old homework problems before they begin the lesson, which goes until the end of class. what fraction of lily's time is spent on the lesson itself?
Lily's time is spent in biology class on lesson is 1 hour or 60 minutes.
Time of one class = 1 hour and fifteen minutes
As we know, 1 hour = 60 minutes
So, time of a class = 60 + 15
Performing addition
Time of a class = 75 minutes
Time spent in talking in biology class = 5 minutes
Time spent in reviewing old homework = 10 minutes
Total time spent = 15 minutes
Remaining time = 75 - 15
Performing subtraction
Remaining time = 60 minutes
Hence, 60 minutes or 1 hour is spent on the lesson.
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What is the slope of a line that is perpendicular to y=4/5x+15 and passes through point (−3, 4)?
Answer:
Step-by-step explanation:
The slope of the line y = -5x-4 is -5 or -5/1 so the slope of the perpendicular line is +1/5 eg…
y = x/5 + c
To find c we substitute x=15, y=-2
-2 = 15/5 + c
-2 = 3 + c
C = -5
So the equation is
Y = x/5 - 5
Two parallel lines are cut by a transversal as shown below.
Suppose m4=124°.
Answer:
156°
Step-by-step explanation:
m5 = m7 (vertical angles)
m4 + m5 = 180 (supplementary)
m5 = 180 - 124 = 156
So measure of both angle 5 and 7 is 156
A model of a car is 1 feet wide and 3 feet long. If the actual car is 15 feet long, what is the width of the actual car?
A. 3 feet
B. 5 feet
C. 15 feet
D. 45 feet
Answer:
5 feet.
Step-by-step explanation:
if we see that 3 feet is the model and 15 feet is the actual, we find the ratio is 3:15 or 1:5. since the width is 1 foot, then we see the actual is 5 feet long.
assume the state of arkansas placed a tax on playing cards of 6 cents per pack. if the state generated $48600 in revenue, how many packs of cards were sold?
The number of pack of cards sold at the state of Arkansas is 8100.
Describe the term division?Multiplication is the complete reverse of division. If participants of 4 add up to 12, then 12 divided into three classes of equally sized results in 4 in each group.For the values given in question.
The tax on playing card in state of Arkansas = 6 cents per pack.
Total revenue generated = $48600.
Divide total revenue by one pack price to get the number of packs.
Number of pack = Total revenue/price of each pack
Number of pack = $48600/6
$48600.Number of pack = 8100
Thus, the number of pack of cards sold at the state of Arkansas is 8100.
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Evaluate the expression:
6² x (16 +19) — 10³
36×(35)-1000=1260-1000=260
Decide whether each equation is true for all, one, or no values of x.
Answer:
Theres nothing to see?
Step-by-step explanation:
Answer:
First is one value of x
Second is no values of x
Third is all values of x
Step-by-step explanation:
Please give brainliest!
The table shows a set of values for x and y
y is inversely proportional to the square x.
a) Find an equation for y in terms of x. (2)
b) Find the positive value of x when y = 25 (2)
Answer:
see explanation
Step-by-step explanation:
(a)
given y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use any ordered pair from the table
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , that is
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is then [tex]\frac{4}{5}[/tex]
Find the Area of the figure below, composed of a parallelogram and two semicircles. Round to the nearest tenth place.
Answer:
550.4 square units.
Step-by-step explanation:
This problem is easier than it seems.
To find the area of the parallelogram, multiply 11 and 32 to get 352 sq. units
The two semicircles must be equal because the sides of a parallelogram must be equal.
So if you add the semicircles together, you get a circle.
So we're really finding parallelogram+circle.
The area of a circle is [tex]\pi[/tex]x[tex]r^{2}[/tex], and the circle's radius is 8 because the radius is half of the diameter.
[tex]\pi[/tex]≈3.1 because you're rounding to the nearest tenth.
3.1x64=198.4 sq. units
198.4+352=550.4 square units.
What is the area of the parallelogram shown?
A= In^2