4
Step-by-step explanation:
3×3+12x=2×2+8
9+12x=4+8
9+12x=12
12x=12-9
12x=3
x=4Use the following values to evaluate the expression (Will give 69 points)
w = 5, x = 9, y = 2
3. x + 20 - 1
A. 28
B. 19
C. 30
D. 32
(Conexus student)
The solution to the given expression (x + 20 - 1) when x = 9 is: A. 28.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In this exercise, you're required to evaluate the given expression and determine its solution. Therefore, we would evaluate the given expression as follows:
x + 20 - 1
Substituting the value of x into the given expression, we have:
Expression = 9 + 20 - 1
Expression = 29 - 1
Expression = 28.
In conclusion, we can reasonably and logically deduce that 28 is the solution to this expression (x + 20 - 1).
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Answer:
a) 28
Step-by-step explanation:
Now we have to,
→ evaluate the expression.
The expression is,
→ x + 20 - 1
Solving the expression,
→ x + 20 - 1
→ 9 + 20 - 1
→ 9 + 19
→ 28
Hence, solution is 28.
Fred, Max, and Ken went trick or treating. Fred had 2 bags of candy with 45 pieces each. Max had 3 bags with 20 pieces each and Ken had 4 bags of candy with 15 pieces each. The boys combined the candy and shared it among 12 people. How much candy is leftover?
Answer:
6 pieces of candy will be left.
Step-by-step explanation:
45×2 = 90
20×3 = 60 +
15×4 = 60
Ttl. of candies= 210
Candies ÷ people
210 ÷ 12 = 17.5
17-12= 5.5 (round to the tenth) 5.5-> 6
210-6= 204
you'll get 6 as the difference which is your answer.
For which interval(s) is the function increasing and decreasing?
y = |2x^2+x-6|
From the graph of the function, it's behavior on the intervals is given as follows:
Increasing: x >0.Decreasing: x < 0.When a function is increasing?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast" along the xy-plane, that is, to the right and up on the graph, meaning that when x increases, y increases.
Hence, from the graph of the function, it is increasing for the values to the right of x = 0, that is, on the interval x > 0.
When a function is decreasing?Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast" along the xy-plane, that is, to the right and down on the graph, meaning that when x increases, y decreases.
Hence, from the graph of the function, it is decreasing for the values to the left of x = 0, that is, on the interval x < 0.
The graph of the function is shown at the end of the answer.
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solve similar triangles (advanced) khan academy. solve for x
The length of the unknown side of the triangle using similar triangle ratio concept is; x = 24
How to Solve similar triangles?We want to find the length of the unknown side of the similar triangles.
Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. Thus, we can say that if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the given triangle ADE which is divide into a similar triangle ABC with an unknown side x, we can use the concept of similar triangle ratios to get the unknown value of x as;
6/x = 8/(x + 8)
Cross multiply to get;
6(x + 8) = 8x
6x + 48 = 8x
8x - 6x = 48
2x = 48
x = 48/2
x = 24
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Can you help break this down. I do not understand at all
Given:
There is an expression given in the question as,
[tex]4x-2(3x-9)[/tex]Required:
We need to find the equal equation in the given option.
Explanation:
First we simplify the given equation
[tex]\begin{gathered} 4x-2(3x-9) \\ =4x-6x+18 \\ =-2x+18 \\ =18-2x \end{gathered}[/tex]Final answer:
[tex]18-2x[/tex]
1) The probability of getting exactly three girls in a family of five children.
2)The probability of getting at least two boys in a family of seven children.
3) The probability of getting a total of 15 when four dice are thrown.
4) Assume that ten percent of us are left-handed. The probability of getting at least two left-handed people in a group of 7.
5) The probability that when 75 people are surveyed, at least five of them have the same birth date. (Ignore leap years).
Using the binomial distribution, the probabilities are given as follows:
1) Three girls in a family of five children: 0.3125 = 31.25%.
2) At least two boys in a family of seven children: 0.9375 = 93.75%.
3) Total of 15 when four dice are thrown: 0.1080 = 10.80%.
4) At least two left-handed people in a group of 7: 0.1497 = 14.97%.
5) At least five of them have the same birth date: 0%.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C(n,x).p^{x}.(1-p)^{n-x}[/tex]
[tex]C(n,x) = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Item 1A children is equally as likely to be a boy or a girl, hence the parameters are given as follows:
n = 5, p = 0.5.
The probability is P(X = 3), hence:
P(X = 3) = C(5, 3) x (0.5)³ x (0.5)² = 0.3125 = 31.25%.
Item 2The parameters are:
n = 7, p = 0.5.
The probability of at least two boys is:
P(X >= 2) = 1 - P(X < 2).
In which:
P(X < 2) = P(X = 0) + P(X = 1).
Then:
P(X = 0) = (0.5)^7 = 0.0078.P(X = 1) = C(7,1) x (0.5)^7 = 0.0547.P(X < 2) = P(X = 0) + P(X = 1) = 0.0078 + 0.0547 = 0.0625.P(X >= 2) = 1 - P(X < 2) = 1 - 0.0625 = 0.9375 = 93.75%.Item 3This one is simple probability, number of desired outcomes divided by the number of total outcomes.
When 4 dice are thrown, we have that:
There are 140 outcomes with a sum of 15.There are 6^4 total outcomes.Hence the probability is:
p = 140/(6^4) = 0.1080 = 10.80%.
Item 4The parameters are:
n = 7, p = 0.1.
Hence, similarly to item 2:
P(X = 0) = (0.9)^7 = 0.4783.P(X = 1) = C(7,1) x (0.1) x (0.9)^6 = 0.3720.P(X < 2) = P(X = 0) + P(X = 1) = 0.4783 + 0.3720 = 0.8503.P(X >= 2) = 1 - P(X < 2) = 1 - 0.8503 = 0.1497 = 14.97%.Item 5The parameters are:
n = 75, p = 1/365 = 0.0027.
Then the probability is:
P(X >=5) = 1 - P(X < 5).
In which:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Using a calculator, it is found that P(X < 5) = 1, hence the probability is of 0%, as P(X >=5) = 1 - 1 = 0.
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What is the domain of this function?
(-1 3 5) (2 6 8)
A. (2, 6, 8, 3, 5)
) B. {2, 6, 8)
O C. (-1, 3, 5)
) D. {3}
The domain of the function is (-1, 3, 5).
Hence the correct answer is Option(C).
What is the domain of a function?Inputs are assigned outputs by functions."All the values" that are input into a function are referred to as the domain of a function. The collection of all potential inputs for a function is its domain.Think of this box as the f(x) = 2x function.The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.However, f(x) = 2x is typically defined for all real values of x, and as a result, its domain is the set of all real numbers, which is denoted by (-∞, ∞).Given function: (-1 3 5) (2 6 8).
Domain is the input values in a function i.e. here it is (-1 3 5).
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A bond with a face value has a current yield of 7% and a coupon rate of 8%. What is the bonds price?
Using it's formula, the bond's price in the context of this problem is given as follows: $5350.
How to calculate the bond's price?To calculate the bond price, we need to know the face value(given in the missing information subsection at the end of the answer) and the yield rate, given at the problem.
The bond price is the given by the multiplication of the face value and 100% plus the yield, hence, in the context of this problem, it is given as follows:
Bond Price = 5000 x 1.07 = $5350.
What is the missing information?The complete problem is given as follows:
"A bond with a face value of $5,000 has a current yield of 7% and a coupon rate of 8%, what is the bonds yield?"
As the face value is needed to calculated the bonds price.
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may anyone help me please?
Answer: 20 is the answer hope you have a great day
!!!!!
Step-by-step explanation:
A bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months. Find the interest rate.
If the bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months, then the interest rate is 30%
The initial amount = $1100
The final amount = $1265
So simple interest = 1265-1100
= $165
Time period = 6 months = 6/12 years
We know
Simple interest I = P×r×t
Where P is the initial amount
r is the interest rate
t is the time period
Substitute the values in the equation
165 = 1100×r×(6/12)
165 = 550×r
r = 165/550
r = 0.3
r = 30%
Hence, If the bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months, then the interest rate is 30%
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How many people would it be if I did 1.2% of French speakers and 5,053,004, representing the whole population? I needed help on calculating how many people it would be with those two numbers.
60,636.048 people are french speakers when the population is 5,053,004 and only 1.2% are the french speakers.
What is Percent?Percentages are basically fractions with a denominator of 100. We use the percent symbol (%) beside a number to indicate that it is a percentage. A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; thus, 100 percent represents the entire amount.
What is method to calculate the percent?To manually calculate percentages, follow these steps:
1. Determine the number's initial format to be converted to a percentage.
The decimal or fraction format of the number to be converted to a percentage can be used. The next mathematical process to be performed on the number will be determined by the initial format.
2. Perform a mathematical calculation on the number to be converted to a percentage.
If the number to be converted to a percentage is a decimal number, such as 0.57, you may not need to proceed to the next step.
3. Multiply the result by 100.
To convert a decimal number, such as 0.57, to a percentage, simply multiply it by 100.
here we need to calculate 1.2% of 5053004
(1.2*5053004)\100
=60636.048
60636.048 people speak french in the country with population of 5053004.
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A staff member lives in Bermondsey and has to be in Birmingham for 10.45 am. It will take her an hour from her home to get to Euston station, for Birmingham train. The journey from Euston to Birmingham takes an hour and ten minutes.Trains to Birmingham run at 5 minutes past the hour, 25 minutes past the hour and 45 minutes past the hour. The venue is a 5-minute walk from the station. What is the latest time that the staff member can leave home to make it in time for the meeting in Birmingham ?
The latest time that the staff member can leave home to make it in time for the meeting in Birmingham is 8.30 am.
Time
Time is used to quantify, measure or compare the duration of events or the intervals between them, and even, sequence events.
Given,
A staff member lives in Bermondsey and has to be in Birmingham for 10.45 am.
Here we need to find the latest time that the staff member can leave home to make it in time for the meeting in Birmingham
From the given details we know identified that,
The staff members has to be present in Birmingham at 10.45am.
But they are all in Bermondsey, it will take 1 hour 10 mins travel to arrive the destination.
So, the time before 1 hour is 9.35 am.
The travel time between train station from home is 1 hour is,
So, the time is 8.35 am.
Venue distance is 5 minutes from station.
So, when we include this then the time to leave the home is,
=> 8.30 am.
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PLEASE ANSWER QUICKLY
What is -3/4 plus -1/6
Answer:
-11/12
Step-by-step explanation:
A large cooler contains 16 lemonade 5 sprite 10 cans of coke and 9 cans of root beers you randomly pick two cans one at a time (without replacement) what is the probability you don’t get two cans of
The most appropriate choice for probability will be given by-
Probability of not getting two cans of coke is [tex]\frac{49}{52}[/tex]
What is probability?
Probability of an event is the chance of occurance of that event.
Probability is calculated by Number of favourable outcomes divided by total number of outcomes
Here,
Number of lemonades in a cooler = 16
Number of sprite in a cooler = 5
Number of cans coke in a cooler = 10
Number of cans of root beers in a cooler = 9
Total number of refreshments = 16 + 5 + 10 + 9
= 40
Probability of getting a can of coke in the first draw = [tex]\frac{10}{40}[/tex]
= [tex]\frac{1}{4}[/tex]
Probability of getting a can of coke in the second draw = [tex]\frac{9}{39}[/tex]
= [tex]\frac{3}{13}[/tex]
Probability of getting two cans of coke in the two draws = [tex]\frac{1}{4} \times \frac{3}{13}[/tex]
= [tex]\frac{3}{52}[/tex]
Probabilty of not getting two cans of coke in the two draws = [tex]1-\frac{3}{52}[/tex]
= [tex]\frac{52-3}{52}[/tex]
= [tex]\frac{49}{52}[/tex]
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Find the volume of composite solid.
The volume of the given cylinder is 37.68ft³.
What is a cylinder?The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. The right cylinder is created when the centers of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centers. Real-world examples of cylinders include toilet paper rolls and cold beverage cans.So, according to the given image, the given solid is a cylinder.
The formula for the volume of cylinders is V = πr²hHeight is 3ft and D is 4ft so r will be 2 ft.Now, insert values in the formula as follows:
V = πr²hV = π2²3V = π4(3)V = 12πV = 37.68 (Let, π be 3.14)Therefore, the volume of the given cylinder is 37.68ft³.
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Select the 3 options below that are equal in value. For example, if one of the terms
equals 0.85, so do the other two.
sample size
area under the curve
proportion
probability
One of the terms equals 0.85, so do the other two:
sample size
proportion
probability
How can sample size be determined?
to calculate the sample size in five easy steps
Define population size or total population.Indicate your error margin.You should assess your level of confidence.Calculate the anticipated variance.finalize the size of your sampleCalculating sample size requires knowledge of or estimation of three or four factors:
the effect size (often the difference between two groups); the population standard deviation (for continuous data); the required power of the experiment to detect the supposed effect; the significance threshold.To learn more about sample size refer to:
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1=0.76r-9-0.36r[tex]1 = 0.76r - 9 - 0.36r[/tex]
Do you have a picture of your question?
Send it please
ok, ready
1 = 0.76r - 9 - 0.36r
1 + 9 = 0.76r - 0.36r
Simplify like terms
10 = 0.4r
Solve for r
r = 10/0.4
r = 25
Result
r = 25
b)
[tex]\begin{gathered} \text{ -5 = }\frac{1}{4}z\text{ - 20 + }\frac{1}{2}z \\ \text{ -5 + 20 = }\frac{1}{4}z\text{ + }\frac{1}{2}z \\ \text{ 15 = }\frac{1\text{ + 2}}{4}z \\ \text{ 15 = }\frac{3}{4}z \\ \text{ 15x4 = 3z} \\ \text{ 60 = 3z} \\ \text{ z = }\frac{60}{3} \\ \text{ z = 20} \end{gathered}[/tex]Result
z = 20
HELP PLEASEEEEEEEEEEEEEE
Using equation;
The monthly payment is 67.5 dollars
The hours of labour that is required to replace the water pump is 4 hours
How to use equation to solve a problem?The purchase of the large TV including finance charges is 1615 dollars . A down payment of 400 dollars was paid. The remainder was paid in 18 monthly instalment payment.
Therefore, using equation,
let
x = amount paid each month
The monthly payment can be found as follows:
1615 = 400 + 18x
1615 - 400 = 18x
1215 = 18x
divide both sides by 18
x = 1215 / 18
x = 67.5 dollars
Therefore,
monthly payment = 67.5 dollars
The cost of replacing a water pump was 465 dollars. This include 145 dollars for water pump plus 80 dollars per hour for labour .
The number of hours for labour that was used to replace the water pump can be calculated as follows:
Using equation,
465 = 145 + 80h
where
h = number of hours for labour
465 - 145 = 80h
320 = 80h
h = 320 / 80
h = 4 hours
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The sun of two rational numbers is 17/4. If one of the numbers is 5/2 find the other number
Answer:
Sum of two rational no. = 17/4
One rational no. = 5/2
So, Let the other rational no. be "x".
Therefore,
\begin{gathered} = > \frac{5}{2} + x = \frac{17}{4} \\ \\ = > x = \frac{17}{4} - \frac{5}{2} \\ \\ = > x = \frac{17 - 10}{4} \\ \\ = > x = \frac{7}{4} \end{gathered}=>25+x=417=>x=417−25=>x=417−10=>x=47
Answer:
Hope the picture will help you
MAKE CONNECTIONS For AC, select an equation you can use to find AB.
O A) 1.5 + 3.7 = AB
O B) AB + 3.7 = 1.5
O c1.5 + AB = 3.7
O D) 1.5 - AB = 3.7
The correct connections for AC will be option b) AB+3.7 = 1.5. Two expressions joined by the equals symbol ("=") form an equation.
What is meant by equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. We determine the value of the variable x as x = 7 by solving this equation.Identity equations and conditional equations are the two types of equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.Different types of equationEquation with a line.Extreme EquationEquation with exponents.Equation with logic.Hence, The correct connections for AC will be option b) AB+3.7 = 1.5.
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Please answer please please
Suzanne is going to rent a car while she is out of town. The car rental company offers a flat rate of $35 plus $0.10 per mile. If she paid $105, then how many miles did she drive?
Answer: 700
Step-by-step explanation:
105-35=70
0.10Xx=70
x=700
700
Suppose the current cost of gasoline is $3.10 per gallon. Find the current price index number, using the 1975 price of 56.7 cents as the reference value.
The current price index is _____
(Round to one decimal place as needed.)
The current price index is mathematically given as,
$538.194
This is further explained below.
What is the current price index?The index value may be calculated by taking the ratio of the current value to the reference value and multiplying that ratio by 100.
In regard to this issue, we have that:
Current value = $3.10
Reference value: $0.576
Generally, the Index price for the is mathematically given as,
I = (3.10/0.576)*100
I= $538.194
The current price index number is 538.194
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Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed?
Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed?
_______________________________________________________
Food ÷ amount of food per dog
5 1/2 pounds of dog food ÷ 1/3
5 1/2 ÷ 1/3 = (10/2 +1/2) ÷ 1/3 = 11/2 ÷ 1/3 = 11/2 x 3/1 = 33/ 2
33/ 2 = 16 1/5 = 16.5
_______________________________________
Can you see the updates?
___________________________________
Answer
She can feed 16.5 (16) dogs with 5 1/2 pounds of dog food
_________________________________________
Do you have any questions regarding the solution?
Write the angle relationship for each pair of angles
Types of angles are given below
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. The plane that contains the rays is where two rays' angles are located. Two planes intersecting at an angle also produces an angle. We call to these as dihedral angles.
Given Data
∠1 and ∠4 are vertical opposite angles.
∠2 and ∠7 are alternate exterior angles.
∠4 and ∠8 are corresponding angles.
∠3 and ∠5 are co interior angle.
∠6 and ∠8 are co linear angles.
∠1 and ∠7 are alternate exterior angle.
∠3 and ∠6 are alternate interior angle.
∠1 and ∠3 are co linear angle.
∠2 and ∠6 are corresponding angles.
∠6 and ∠7 are vertical opposite angle.
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As part of your job you spend time each day contacting former customers. During one week, you contacted 15 people on Monday, 12 on Tuesday, 14 on Wednesday, 11 on Thursday, and 13 on Friday. What is the average number of customers contacted each day? Which averaging method did you use?
The average number of customers contacted each day is 13. We used the basic average method which is explained below.
The formula for calculating the average is:
Sum of all the observations ÷ Total number of observations
So, according to the formula
Sum of all the observations = People contacted on (Monday+ tuesday+wednesday+thursday+friday)
= 15+12+14+11+13
= 65
Number of observations = 5
So putting values in the formula, we get
65÷5
= 13
Hence, the average number of customers contacted is 13.
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Trapezoid W’X’Y’Z’ is the image of trapezoid W’ X’ Y’ Z’ under a dilation though point c
The scale factor used in the dilation through point c is 3/4.
Using the Scale Factor, shapes in various dimensions can be scaled. In geometry, we examine a wide variety of two- and three-dimensional geometrical forms.
Comparing figures with similar appearances but different scales or measures is possible using the scale factor. Take into account two circles that resemble one another but could have various radii. The scaling factor shows how much a figure has grown or shrunk from its starting point.
Any original shape can be designed as an extended or condensed version by using a scaling factor. In the equation y = Kx, K is the scaling factor for x.
The scale factor formula is provided by:
dimensions of the first form x scale Factor = Dimension of new shape
Scale factor equals Dimension of New Shape divided by Dimension of Original Shape
Given, dimension of trapezium WXYZ = 8 m
Dimension of trapezium W'X'Y'Z' = 6 m
Using above literature and necessary assumptions:
WXYZ * scale factor = W'X'Y'Z'
Therefore, scale factor = W'X'Y'Z'/WXYZ ⇒ scale factor = 6m/8m = 3/4
Thus, the scale factor is 3/4.
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Can someone please help I give lots of points...
Answer:
y=-x^2+16x-55
Step-by-step explanation:
Since two intercepts are given (the two x-intercepts in this case), we should probably use intercept form.
y=a(x-b)(x-c)
plug in the intercepts which are 5 and 11 in this case
y=a(x-5)(x-11)
to solve for a, use the remaining point and set x to 6 and y to 5. we can do this because (6,5) is given to us as a solution of one of the points on the graph.
5=a(6-5)(6-11)
5=a*(-5)
a=-1
so, the equation should be:
y= - (x-5)(x-11)
expand the parentheses to get:
y=-x^2+16x-55
(also 5 points isn't a lot of points...)
Write down equation of lines l and m
Step-by-step explanation:
I assume you need the slope-intercept form
y = ax + b
"a" is the slope of the line, "b" is the y- intercept (the y-value when x = 0).
the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
for l we go from (5, 20) to (8, 80) and get
x changes by +3 (from 5 to 8)
y changes by +60 (from 20 to 80)
the slope is therefore
+60/+3 = 20/1 = 20 = a
so, we have
y = 20x + b
the y- intercept looks to be -80, but to be sure we use a point (e.g. 5, 20)
20 = 20×5 + b = 100 + b
b = -80
yes, the equation is
y = 20x - 80
for m we go from (5, 20) to (8, -40) and get
x changes by +3 (from 5 to 8)
y changes by -60 (from 20 to -40)
the slope is
-60/+3 = -20/1 = -20
we have therefore
y = -20x + b
we use the same trick for b as before
20 = -20×5 + b = -100 + b
b = 120
and our full equation is
y = -20x + 120