The value for the height of the rectangular prism is found as; h = 7.
What is defined as the rectangular prism?A rectangular prism is a three dimensional solid shape with six faces that have rectangles as their bases. Right rectangular prisms as well as non-right (oblique) rectangle prisms are the two types of rectangular prisms. The right rectangle prism does have two parallel end faces and 4 lateral faces, each of which is an rectangle; this same faces are perpendicular to the bases of the prism.The formula for the surface area of rectangular prism is;
S = 2(ab+bh+ah)
Where,
a=6, b=5 and s=214
Substitute the values in the formula.
214 = 2(6×5 + 5h + 6h)
Simplifying;
30 + 11h = 107
11h = 107 - 30
11h = 77
h = 7
Thus, the value for the height of the prism is found as; h = 7.
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Solve the following system of equations:
x -2y = 18
4x + 3y = -16
What's the (x,y) coordinates
Step-by-step explanation:
Solve for X for one equation then input that value into the other equation.
x+2y=9
x=9-2y
x-y=3
(9-2y)-y=3
9-3y=3
6=3y
y=2
x=5
The value of the y-coordinate of the system of equations is y=2.
I hope it help
Find the expected payback for a game in which you bet $10 on any number from 0 to 999. If your number comes up, you get $2000
The expected payback is mathematically given as
$10
This is further explained below.
What is the expected payback?Generally, The formula for calculating the anticipated payback is the product of the likelihood times the value.
E(x) = p(x_1)*x_1 + p(x_2)*x_2 + .....
In this particular scenario, we have two distinct options for repayment.
winning
The payback is $2000-$10 = $1990
x_1 = 1990
The probability of winning is one out of 100 (since the choices are 0 to 99)
p(x_1) = 1/100
Losing
The payback is negative $8 since the individual did not win anything, which makes them lose.
x_2 = -10
Because there is only one number that can win, the other 99 numbers are considered to be losing numbers.
p(x_2) = 99/100
Therefore expected payback is
E(x) = p(x_1)*x_1 + p(x_2)*x_2
= (1/100)* 1990+ (99/100)*(-10)
= $10
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CQ
Find the expected payback for a game in which you bet $10 on any number from 0 to 999. If your number comes up, you get $2000
The expected payback is
Solve for c.
a(c+b) = d
Answer: C=D\A-B THAT IS THE ANSWER
Step-by-step explanation:
The height of a triangle is 5 centimeters greater than the base. The area of the triangle is 63 square centimeters. Find the length of the base and the height of the triangle.
The base and height of the triangle are 9 cm and 14 cm respectively.
How to find the side of a triangle?The height of the triangle is 5 centimetres greater than the base.
The area of the triangle is 63 cm².
Therefore,
area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
h = 5 + b
Hence,
area of a triangle = 1 / 2 × b × (5 + b)
area of a triangle = 1 / 2 × 5b + b²
63 = 5b + b² / 2
cross multiply
126 = 5b + b²
b² + 5b - 126 = 0
b² + 14b - 9b - 126 = 0
b(b + 14) - 9(b + 14) = 0
(b + 14)(b - 9) = 0
b = -14 or b = 9
Therefore, the base can only be positive .
Hence,
Base of the triangle = 9 cm
height of the triangle = 9 + 5 = 14 cm
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B.E.S.T. TEST PREP Which of the following values of x and y make the relation a function? Select all that apply.
( − 3, 7), ( – 2, 3), (0, 8), (1, − 1), (x,y)
O x=-4, y = 0
0
x = 1, y = -2
O x = 5, y = -1
O x=2, y = 8
G
The x and y values that makes the relation a function are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8
How to determine the values of x and y?The ordered pairs are given as
(− 3, 7), (–2, 3), (0, 8), (1, − 1), (x,y)
For a list of ordered pairs to represent a function, the following must be true
The x values must have exactly one y value
Using the above as a guide, we can see that x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8 fits the above description
Hence, the values of x and y are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8
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I need answer for this question
The probability that the aircraft is overloaded is 97.98%, which means the pilot should take the action.
In a Normal distribution with mean ц and standard deviation σ, the z-score of a measure x is given by:
Z = X-ц / σ
· It measures how many standard deviations the measure is from the mean.
· After finding Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
· By the Central Limit Theorem, the sampling distribution of sample means of the size n has standard deviation σ
σ = σ / [tex]\sqrt{n}[/tex]
σ is standard deviation
n is the sample size.
Given that the mean and the standard deviation of the population is 176.1 lb and 35.4 respectively.
⇒ ц = 176.1 and σ = 35.4
For a sample of 43 passengers, we have
n = 43
σ = [tex]\frac{35.4}{\sqrt{43}}[/tex]
σ = 5.398
Z = X-ц / σ
Z = [tex]\frac{165-176.1}{5.398}[/tex]
Z = -2.05 has p- value of 0.9798
The probability that the aircraft is loaded is
1 - p-value of Z
1 - 0.0202 = 0.9798
The probability that the aircraft is overloaded is 97.98%
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what is the permiter in feet of a rectangle with height 4 1/6 feet and width 3 1/3
The perimeter in feet of a rectangle with height 4 1/6 feet and width 3 1/3 is 15 feet.
How to calculate the perimeter?It should be noted that the perimeter of a rectangle is calculated thus:
Perimeter = 2(Length + Width).
Based on the information, the following can be deduced:
Length = 4 1/6 feet
Width = 3 1/3 feet
Perimeter = 2(Length + Width).
Perimeter = 2(4 1/6 + 3 1/3)
Perimeter = 2(7 1/2)
Perimeter = 15 feet
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REDUCING RATIOS
1. 55:33
2. 1,000:100
3. 560:80
4. 20:340
Answer:
Step-by-step explanation:
1. 5:3
2. 10:1
3. 7:1
4. 1:17
Assume that 40% of a country's population has had Covid and that 55% of the country's population has been vaccinated. There is some overlap between the two groups, and 25% of the country's population has both had Covid and has also been vaccinated. Either having Covid or being vaccinated gives some protection against getting Covid. Based on these assumptions, if you choose a resident of this country at random what is the probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid?
The probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid is 45%
Data obtained from the questionFrom the question given, the following data were obtained:
40% of a country's population has had Covid55% of the country's population has been vaccinated25% of the country's population has both had Covid and has also been vaccinatedHow to determine the required probabilityThe probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid can be obtained as follows:
The percentage of person that had Covid and not vaccinated
= 40% - 25%
= 15%
The percentage of person that has been vaccinated and never had Covid
= 55% - 25%
= 30%
The probability that the person has either had Covid or has been vaccinated
= 15% + 30%
= 45%
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Mean of 20 observations is 17. If in the observations, observation 40 is replaced
by 12, find the new mean.
Please help
The new mean is 18.4
According to the question,
The mean of 20 observations is 17
So the total value of all the observations = 20*17
= 340
The new value will be = 340 +40-12
= 368
Then,
The new mean of 20 observations will be= 368÷20
= 18.4
Hence, the new mean is 18.4
Mean is the average of a set of two or more numbers. It is of two types; arithmetic mean and geometric mean. It is part of statistics.
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what's the difference AAA,ASA and SSS
There are three main distinctions between AAA, ASA, and SSS:
AAA: A triangle is said to be comparable to another if any two of its three angles are equal to any two of its three angles.
ASA: According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and the side located between the angles of the second triangle.
SSS: According to the SSS rule, two triangles are considered to be congruent if all three sides of one triangle are comparable to the corresponding three sides of the other triangle.
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The sum of two numbers is 96. The difference of the two numbers is 42. What are the two numbers.
Let
x
be the larger number and
y
be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 96."
Correct
Write an equation that expresses the information in the sentence "The difference of the two numbers is 42."
Correct
Solve the system you have written above.
The larger number,
x
is
Correct. The smaller number,
y
is
Correct.
Question HelpQuestion 1: Message Message instructor
Submit QuestionQuestion 1
Using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27
Consider the largest number as x and the smallest number as y
The sum of two numbers is 96
The equation will be
x+y = 96
x = 96-y
The difference of the two numbers 42
x-y = 42
Use the substitution method here
Substitute the value of x in the second equation
x-y =42
(96-y)-y =42
96-2y = 42
-2y = 42-96
-2y = -54
y = 27
Substitute the value of y in the first equation
x+y = 96
x+27 = 96
x = 96-27
x = 69
Hence, using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27
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Factor the following expression. x^2+17x+60
nswer:
[tex](x+12)(x+5)[/tex]Explanation:
iven the below expression;
[tex]x^2+17x+60[/tex]We'll follow the below steps to factor the given expression;
tep 1: L
The factors are 12 and 5. We'll go ahead and replace the middle term 17x with these factors as seen below;
[tex]x^2+12x+5x+60[/tex]tep 2: GG
[tex](x^2+12x)+(5x+60)[/tex]tep 3: F
[tex]x(x+12)+5(x+12)[/tex]tep 4: FW
[tex](x+12)(x+5)[/tex]Differentiate the function f(x)=sinx/(1+tanx)
Differentiation of the given function f(x)=sinx/(1+tanx) is equal to
(cos³x -sin³x) / (cos²x)(1 + tanx)².
As given in the question,
Given function : f(x) = sinx /(1 + tanx )
Let u = sinx , v = ( 1 + tanx)
Differentiate the given function with respect to x
du/dx = cosx
dv/dx = sec²x
= 1/cos²x
(d/dx)(f(x)) = (d/dx)(sinx /(1 + tanx ))
= ( d/dx) (u / v)
= [v (du/dx) -u (dv/dx)] / (v)²
= [(1+tanx)(cosx) -(sinx)(1/cos²x)] / (1 + tanx)²
= [cos²x(cosx + sinx) -sinx]/ (cos²x)(1 + tanx)²
= [cos³x +sinx(cos²x -1)] / (cos²x)(1 + tanx)²
= (cos³x -sin³x) / (cos²x)(1 + tanx)²
Therefore, differentiation of the given function f(x)=sinx/(1+tanx) is equal to
(cos³x -sin³x) / (cos²x)(1 + tanx)².
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A computer password is required to be 7 characters long. How many passwords are possible if the password requires 2 lowercase letter(s) followed by 5 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
We will see that there are 19,656,000 different passwords that can be made with the given characters.
How many passwords are possible?We need to find the number of possible options for each character of the password.
The first character is a letter, so we have 26 options.
The second character is another letter, so we have 25 options (because we can't repeat).
Then we have 5 digits, for each digit we have 10 options (removing one for each subsequent one)
First digit: 10 options.Second digit: 9 options.Third digit: 8 options.Fourth digit: 7 options.Fifth digit: 6 optionsThe total number of passwords is given by the product between the numbers of options.
P = 26*25*10*9*8*7*6 = 19,656,000
There are 19,656,000 different passwords that can be made.
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Of all the people who attended the school
play, 65% were parents of children in the
play. If the total attendance was 500 people,
how many were parents of children in the
play?
Answer:
Step-by-step explanation:
Total attendance = 500 people
Parents of children in play = 65% of 500
=>0.65 * 500
=> 325
325 were the parents of children in the play.
13. Highlight the answer choice that represents the distance between the two points below. Round to the nearest hundredth if necessary. You may use a calculator.
A. 10
B. 28
C. 3100
D. 10
E. 310
F. 3.16
Supposing that the two points are (2,4) and (10,10), the distance between them is given by:
A. 10.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.
For this problem, the two points are (2,4) and (10,10), hence the distance between them is given as follows:
[tex]D = \sqrt{(10 - 2)^2+(10 - 4)^2} = \sqrt{100} = 10[/tex]
Hence the distance is of 10 units and option A is correct.
What is the missing information?This problem is incomplete, and I could not find it on any search engine, hence we are going to suppose that the two points are (2,4) and (10,10).
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one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x
The value of the expression one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x is 2 - 2/15x.
How to illustrate the information?It should be noted that expressions are simply used to show the relationship that exists between the variables that are given.
In this case, one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x will be illustrated as:
= 1/5(3x + 10) - (11/15x)
= 3/5x + 2 - 11/15x
= 9/15x + 2 - 11/15x
= 2 - 2/15x
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There are 90 students total in the sixth grade. 45 of those students are girls. What percent of the students in the sixth grade are girls?
Answer: 50%
Step-by-step explanation:
when you divide 90 by 2 you get 45 so 45+45=90
Answer: 8% of the students in the sixth grade are girls
Step-by-step explanation:
Simplify and write your answer with a positive exponent
Riders for the Kiddie Koaster at the State Fair must be no more than 48 inches tall. Which inequality best expresses the height of the riders?
[tex]x \leqslant 48[/tex]
If 3x = 21 find the value of x-8
PLEASE HELPPPP
x − 8 = − 10
Explanation: 9x −13 = − 31 Add 13 to each side.
Answer:
-1
Step-by-step explanation:
3x = 21
Divide both sides by the co efficient of x
3x = 21
3 3
x = 21/3
x = 7
Find x - 8
x = 7
7 - 8
= -1
Determine the MOST precise bane for quadrilateral PQRS
Solution:
Given:
To get the precise name of the quadrilateral PQRS, using the coordinates of the points given;
The distance between points P and Q, and points Q and R are the same.
Also the distance between points P and S, and points R and S are also the same.
This means;
[tex]\begin{gathered} PQ\cong QR \\ PS\cong RS \end{gathered}[/tex]Hence, the image is as shown;
By the property of a kite, which says that two pairs of consecutive sides are congruent sides.
Hence, the most precise name for the quadrilateral PQRS is a KITE.
100 POINTS TO WHOEVER RESPONDS FIRST!!!!
The domain and range of the given inequality graph are; Domain: {x | -2 ≤ x ≤ 2} and Range: {x | -6 ≤ x ≤ 6}
What is the Domain and Range of the Function?The domain of a function is the set of all possible input values that make a function possible. Meanwhile the range of a function is the set of all possible output values that make a function possible.
Now, when dealing with an inequality graph, it is pertinent to note that a shaded dot implies less than or equal to (≤) or greater than or equal to (≥) while unshaded means less than or greater than.
Now. the range of the graph is closed from y = -6 to y = 6. Thus, the range is; {y| -6 ≤ y ≤ 6}
Meanwhile the domain of the graph is closed from x = -2 to x = 2. Thus, the domain of the graph is;
{x | -2 ≤ x ≤ 2}
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Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow \infty }-\frac{3x^2}{x^2\ +4}[/tex] as x approaches ∞ is -3
What is limit?A limit is the value that a function, sequence, or index approaches as an input or index approaches a specified value in mathematics. Limits are required in the definitions of continuity, derivatives, and integrals, which are essential in calculus and mathematical analysis.
The notion of a limit of a sequence is further generalized to include the notion of a limit of a topological network, in addition to being closely related to the concepts of limit & direct limit in category theory.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
⇒ [tex]\lim_{x\rightarrow \infty }-\frac{3x^2}{x^2\ +4}[/tex]
⇒ [tex]\lim_{x\rightarrow \infty }-\frac{6x}{2x + 0}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{-6x}{2x }[/tex]
Evalúe ∞ as x
⇒ [tex]\frac{-6(\infty)}{2(\infty)} }[/tex]
⇒ -3
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what is perpendicular consider of?
Answer: straight line that makes the right angle (90 degrees) with the other
Step-by-step explanation: In other words, if two lines intersect each other at the right angle, then the lines are perpendicular to each other
5 (x² − 2) + 2x − 3x (x − 7)?
I just need help with the working it out step.
Answer:
[tex]2x^2+23x-10[/tex]
Step-by-step explanation:
1) distribute the parenthesis by multiplying 5 into (x^2 - 2) and -3x into (x - 7)
[tex]5x^2-10 +2x-3x^2+21x\\[/tex]
2) simplify by adding and subtracting like terms
[tex]2x^2+23x-10[/tex]
I need help with a geometry problem, but I cannot type it out i will need to send a picture of it
From the triangle given, we are required to solve for x and y.
Since they are similar triangles, let's find x and y below.
For x:
[tex]\frac{5}{8}=\frac{5+x}{10}[/tex]Let's find x, from the equation above.
Cross multiply:
[tex]\begin{gathered} 8(5+x)=10(5) \\ \\ 40+8x=50 \\ \\ \text{Subtract 40 from both sides:} \\ 40-40+8x=50-40 \\ \\ 8x=10 \end{gathered}[/tex]Divide both sides by 8:
[tex]\begin{gathered} \frac{8x}{8}=\frac{10}{8} \\ \\ x=1.25 \end{gathered}[/tex]For y:
[tex]\begin{gathered} \frac{7}{8}=\frac{7+y}{10} \\ \\ 8(7+y)=7(10) \\ \\ 56+8y=70 \\ \\ 8y=70-56 \\ \\ 8y=14 \\ \\ \frac{8y}{8}=\frac{14}{8} \\ \\ y=1.75 \end{gathered}[/tex]ANSWER:
x = 1.25, y = 1.75
The following relations describe monthly demand and supply relations for dry cleaning
services in the metropolitan area?
Qd = 500000 – 50000P
Qs = -100000 + 100000P
A, Calculate the market equilibrium price/output combination, show graphically
B, Calculate the surplus or shortage when P=3 and P= 6
C, Calculate price elasticity of demand at equilibrium price
It is to be noted that at the equilibrium level, the Equilibrium price/output combination is $4 and 300,000 units respectively. See further calculations and answer below.
What is the Equilibrium level?Recall that the equilibrium level of the national income is defined as that point where the aggregate supply (QS) and the aggregate demand (AQD) are the same.
To calculate the market equilibrium price/output combination (EQL:
Step I - Recall the given data
Recall that at EQL, QD = QS
Where:
Qd = 500000 – 50000P; and ....................1
Qs = -100000 + 100000P. ...........................2
Hence, at EQL,
500000 – 50000P = -100000 + 100000P
⇒ 150,000P = 600,000 [divide both sides by 150,000
⇒ P = 600,000/150,000
⇒P = $4
Step II
To get Q, substitute P into (1)
thus, we have:
500,000 – 50000 (4)
500,000 – 200,000
= 300,000 units.
Hence, at EQL, P = $4 and Q = 300,000 units.
B)i What is P = $3?
Recall Step II above,
Simply substitute $3 into (1)
⇒ 500,000 – 50,000 (3)
= 500,000 – 150,000
= 350,000 units
ii) what is P = $6, just repeat the above steps to get
200,000 units.
C) Price Elasticity of Demand (PED) at Equilibrium Price
The PED is the percentage change in the quantity requested as a result of a 1% change in price. The PED coefficient is often negative, although economists frequently overlook the sign. If the PED coefficient is less than one, demand for an item is generally inelastic (in absolute value).
The formula for demand (PED) at P = 6 is determined using the formula:
PED = %Δ in QD / %Δ in Price..................1
%Δ in QD = (200,000-300,000)/300,000 ..............2
With 300,000 beings (Original Unit at Equilibrium)
Hence %Δ in QD = -0.333
%Δ in Price = (6-4)/4
= 1/2j or 0.5
PED = -0.333/0.5
PED = |-0.666|
Given that the PED is < 1, we can conclude that the demand for dry cleaning is inelastic.
In a situation where it is greater than 1, then the demand is elastic.
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which sets of ordered pairs are functions and which are not functions? 1. { (1,5),(2,5),(3,5),(4,5) } 2. { (1,5),(1,6),(1,7),(1,8) } 3. { (1,6),(2,5),(2,3),(4,8) } 4. { (1,5),(3,7),(4,8),(4,9) }
Number 2 is not a function, because we have more that one value of x that is the same
Number 3 is also not a function, we have more than one value of x that is the same
Number 4 is also not a function
Therefore, only number 1 is a function