The Mathematical Expression formed is 4(10-8)
What is a Mathematical Expression?
In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations.
Solution:
The mathematical expression formed frrom the statement;
Multiply the difference of 10 and 8 by 4
is as follows,
4(10-8)
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In a photo contest, two judges are giving scores to each photo. Each judge gives a score for impact (worth 40%), composition (worth 30%), lighting (worth 20%), and color balance (worth 10%). Lester entered a photo in the contest and received the following scores: Impact: 8 and 9 Composition: 7 and 7 Lighting: 8 and 7 Color balance: 5 and 7 Enter a number in each box to create an expression that represents Lester's final score.
Lester's final score from the two Judges is 7.6
How to calculate Lester's final scoreThe scores of the judges are in percentage and this will be converted to decimal by dividing by 100
impact (worth 40%) = 0.4
composition (worth 30%) = 0.3
lighting (worth 20%) = 0.2
color balance (worth 10%) = 0.1
Average score from the Judges will be used to multiply the percentages
Impact: 8 and 9
= 8.5 * 0.4 = 3.4
Composition: 7 and 7
= 7 * 0.3 = 2.1
Lighting: 8 and 7
= 7.5 * 0.2 = 1.5
Color balance: 5 and 7
= 6 * 0.1 = 0.6
sum of the scores gives Lester's final score as 7.6
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An auto insurance company charges males 16-18 years old a base price of $1100 for insurance in a given year. Their accuracies have determined that there is a 8.5% a claim will be made against such a policy and an average claim of $4900. What does the insurance company expect to make on average off of each policy holder?
If a claim will be made against such a policy and an average claim of $4900. the insurance company should make on average off of each policy holder is $683.5.
How to find the amount the company should make?Using this formula to find the amount
Amount = [Percentage claim × ( Base price - Average claim)] + [(1 - percentage claim) × Base price]
Let plug in the formula
Amount = [0.085 × ($1,100 - $4,900)] + [(1-0.085) × $1,100]
Amount = [0.085 × (- $3,800)] + [(0.915 × $1,100]
Amount = -$325+ $1,006.5
Amount = $683.5
Therefore the insurance company will make the amount of $683.5.
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Find P(AUB) of P(A)=2/5,P(B)=2/7 and A and B are Independent
P(A∪B)=24/35 when A and B are independent and P(A)=2/5,P(B)=2/7
What is meant by probability?Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty. The greater the likelihood of an occurrence, the more likely it will occur.
Probability theory, which is widely used in domains such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these concepts axiomatic mathematical formalization.
Given,
P(A)=2/5
P(A)=2/7
P(A∪B)=?
And also given that A and B are independent then,
P(A∩B)=0
P(A∪B)=P(A)+P(B)-P(A∩B)
P(A∪B)=(2/5)+(2/7)-0
P(A∪B)=(14+10)/35
P(A∪B)=24/35
Therefore, P(A∪B)=24/35 when A and B are independent.
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Describe a real life siuation for each problem
1. -3 + (-4)
2. -3 (+2)
Answer:
1. I'm $3 in debt, and I spend 4 more dollars. I am now 4 dollars more in debt than I was before.
2. I'm $3 in debt, and I pay back $2 of debt. I am now $1 in debt.
Step-by-step explanation:
-Hope this helped
Differentiate the function with respect to x.
Differentiation of f(x) is [tex]-8x^{3} sinx^{4}[/tex].
Given,
f(x) = [tex]cos2x^{4}[/tex]
Now, we will differentiate f(x) with respect to x,
[tex]\frac{d}{dx}cos2x^{4} = (\frac{d}{dx}cos2x^{4})(\frac{d}{dx}2x^{4} )[/tex]
[tex]= (-sin2x^{4})(2*4x^{3})[/tex]
[tex]= -8x^{3}sin2x^{4}[/tex]
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. You get an auto loan at 3.5% interest for 5 years; please answer the following.
A. You can afford a $250 per month car payment; how expensive a car can you afford?
B. You purchase a car for $8000 with a $2000 down payment, what are your monthly payments?
Using the monthly payment formula, it is found that:
A. You can afford a car at a price of $13,742.36.
B. The monthly payments are of $109.15.
What is the monthly payment formula?The monthly payments are given by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The variables involved in the equation are listed and explained as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For item a, the parameters are given as follows:
A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
Hence the maximum value of the car is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
0.0181919241P = 250
P = 250/0.0181919241
P = $13,742.36
For item b, the parameters are given as follows:
P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).
Hence the monthly payments are given as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
A = 6000 x 0.0181919241
A = $109.15.
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Quinn is baking sweet potato pies. The table shows the ratio of cups of sugar to number of pies.
Number of Pies 3 5 9
Cups of Sugar 1 and one half 2 and one half 4 and one half
How many cups of sugar will Quinn need to make 12 pies?
5 and one half cups
6 cups
6 and one half cups
8 cups
The ratio of 6 cups of sugar to pie that Quinn needs to make 12 potato pies will be 6 cups.
What is ratio?Ratio basically compares quantities, that shows value of one quantity with respect to other quantity.
If a and b are two values, there ratio will be a:b.
Given that,
For 3 potato pies required sugar is 3/2,
For 5 potato pies required sugar is 5/2,
for 9 potato pies required sugar is 9/2,
From the given information,
For 1 potato pies required sugar is 1/2
⇒For 12 potato pies required sugar=12×1/2=6
To make 12 potato pies, required sugar will be 6.
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What is 4/5 ÷ 1/3? The quotient is 2 and
Answer:4/5 : 1/3=4/5 x 3/1=12/5
Step-by-step explanation:
Answer:
12/5
Step-by-step explanation:
If you set it in the calculator 4/5 ÷ 1/3 you get = 12/5
was it helpful?
Hi can someone please help me? Thank you!
589 in base five is
589 in base five is [tex]4324_{5}[/tex].
Given number:
589
converting to [tex]589_{5}[/tex].
⇒ 5|589
⇒ 5|117|4
⇒ 5|23|2
⇒ 5|4|3
⇒ 5|4|4
Now we write the last digit from last number to first that is,
= [tex]4324_{5}[/tex].
Hence 589 in base five is [tex]4324_{5}[/tex].
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The marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation.
-3/4
C'(x)=x
Find the cost of printing 133 more posters when 17 have already been printed.
The cost of printing 133 more posters when 17 have already been printed is $.
(Round to the nearest cent as needed.)
When only 17 posters have been printed, it will cost $ 5. 46to print 143 more.
How to calculate cost of painting?A mathematical formula known as a cost function is used to visualise how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.
The following equation, C'(x)=x-3/4, tells us the marginal cost (in dollars) of printing a poster after x posters have been printed.
The given equation is :C'(x)=x-3/4
The cost of printing 133 more posters when 17 have already been printed is given by;
applying the limitations we obtain and integrating both sides of the equation;
[tex]$$\int_a^b C^{\prime}(x) d x=\int_{17}^{133} x^{\frac{-3}{4}} d x$$[/tex]
As we know that [tex]$\int x^n d x=\frac{x^{n+1}}{n+1}$[/tex], so;
[tex]$&=4\left[x^{\frac{1}{4}}\right]_{17}^{133} \\[/tex]
[tex]$&=4\left[(133)^{\frac{1}{4}}-(17)^{\frac{1}{4}}\right] \\[/tex]
= $ 5.4616
Therefore When only 17 posters have been printed, it will cost $ 5. 46to print 143 more.
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Please help with this table. Not sure why this is difficult
A rotating light is located 17 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
When the the light's angle is 20° from perpendicular to the wall, and the light is rotating at an angular speed of one rotation in 2 seconds the rate the light projected onto the wall is moving is approximately 60.48 feet/s
What is angular speed?Angular speed, ω, is the angle, θ, in radians rotated by a rotating object per second. The unit of angular speed is radians per second, rad/s.
Mathematically;
[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]
Where;
Δt = The time the object rotates through an angle of Δθ
The distance of the light from the wall, x = 17 feet
Time it takes the light to complete one rotation = 2 seconds
Angle the light makes with the perpendicular wall = 20°
[tex]tan(\theta) = \dfrac{y}{x}[/tex]
The distance the light has moved along the wall, y = x × tan(θ)
Therefore;
The y = 17 × tan(θ)
The angular velocity of the light, ω = θ/t
Therefore, θ = ω × t = ω·t
Which gives; y = 17 × tan(ω·t)
[tex]\omega = \dfrac{2\cdot \pi}{2}\ rad/s = \pi \ rad/s[/tex]
Therefore; x = 17 × tan(·t)
[tex]\dfrac{dy}{dt} = \dfrac{d}{dt} \left(17\times tan(\omega\cdot t)\right) = 17\cdot \omega\cdot sec^2(\omega \cdot t)[/tex]
ω = π rad/s (constant)
ω·t = θ
Therefore;
[tex]\dfrac{dy}{dt}= 17\cdot \omega\cdot sec^2(\theta)[/tex]
Rate the light is moving along the wall, dy/dt when θ = 20°, is therefore;
[tex]\dfrac{dy}{dt}= 17\times \pi\cdot sec^2(20^{\circ}) \approx 60.48[/tex]
The light is moving at a rate of 60.48 feet/s when the lights angle is 20 degrees from the perpendicular wallLearn more about angular or rotational speed here:
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which ones bigger -1.35 or -1 4/9 by the way 4/9 is a fraction
Answer:
[tex]-1.35[/tex] is bigger (larger)
Step-by-step explanation:
[tex]-1\frac{4}{9}=-1.\overline{44}[/tex]
Therefore, because [tex]-1.35[/tex] is less negative than [tex]-1.\overline{44}[/tex],
[tex]-1.35[/tex] is bigger (larger).
A square floor is fitted with rectangular tiles of perimeter 220 cm. Each row carries 20 less tiles than each column. If the length of the floor is 9.6 m; calculate
(a) the dimensions of the tiles.
(b) the number of tiles needed.
(c) the cost of fitting the tiles if the tiles are sold in dozens at Kshs. 1500 per dozen and the labour cost is Kshs. 3000.
The 220 cm (2.2 m) perimeter of the tiles and the 9.6 meter side length of the square floor gives equations with the following solutions;
(a) The dimensions of the tiles are;
Width = 0.3 meters
Length = 0.8 meters
(b) 384 tiles are needed
(c) The fitting cost of the tiles is Kshs 51,000
What is an equation?An equation is a mathematical statement that consists of two expressions connected with an equals sign
Shape of the floor = Square
Shape of the tiles = Rectangular
Perimeter of the tiles = 220 cm = 2.2 m
The number of tiles in each row = 20 + The number of tiles in each column
Length of the floor = 9.6 m
(a) Let w represent the width of the tiles, the length l is found using the equation;
[tex]l = \dfrac{2.2 - 2\cdot x}{2} = 1.1 - x[/tex]
Let n represent the number of tiles in each row, which gives;
The number of tiles in each column = 20 + n
(20+n)·x = n·(1.1 - x)
Which gives;
[tex]x = \dfrac{1.1\cdot n}{2\cdot n+20}[/tex]
The side length of the square floor, s = 9.6
(20+n)·x = n·(1.1 - x) = 9.6
Which gives;
[tex]n\cdot \left(1.1 - \dfrac{1.1\cdot n}{2\cdot n+20}\right) = 9.6[/tex]
Which gives;
0.55·n² - 1.4·n -96 = 0
n = 12 or n ≈ -14.5
The number tiles in each roe, n = 20
Which gives; n·(1.1 - x) = 9.6
20 × (1.1 - x) = 9.6
x = 0.3
The width of each tile, x = 0.3 m
The length of each tiles = 1.1 m - 0.3 m = 0.8 m
(b) The number of tiles in each row, n = 20
The number of tiles in each column = n + 20, which gives;
Number of tiles in each column = 12 + 20 = 32
The number of tiles needed = 12 × 32 = 384
(c) The cost of a dozen tiles = Kshs 1,500
The labour cost = Kshs 3,000
Number of dozens of tiles = 384 ÷ 12 = 32
The cost of the tiles C = Kshs 1500 × 32 = Kshs 48000
The total cost = Kshs 48,000 + Kshs 3,000 = Kshs 51,000
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Help Geometry (ASAP!!)
Answer:
yes if b is odd then b+6 is odd
Step-by-step explanation:
example
consider a odd number 1,3,5,7,and 9
1+6=7
3+6=9
5+6=11
7+6=13
9+6=15
all answers are odd number
Pedro and Rebecca were trying to solve the equation:
0.1x^2 - 0.7x + 1.2 = 0
Pedro said, “I can multiply the entire equation by 10 and then factor. Then I can solve using the zero product property.”
Rebecca said, “I'll solve using the quadratic formula with a = 0.1 1, b = -0.7 and c = 1.2"
WHOs Strategy works?
A - Only Pedro's
B - Only Rebecca's
C - Both
D - Neither
The correct strategy between Pedro and Rebecca trying to solve the quadratic equation: 0.1x^2 - 0.7x + 1.2 = 0 is A - Only Pedro's
How to determine the correct strategyThe given function is a quadratic function which is solved by several method including the method both Pedro and Rebecca are trying to use
Pedro's method is the factorization method and the steps mentioned are correct
However Rebecca's method has some error
The equation is: 0.1x^2 - 0.7x + 1.2 = 0
factor of the leading coefficient a is 0.1, Rebecca is using 0.11
The error of using 0.11 instead of 0.1 will make the method ineffective
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Can anyone help me in this question? pls.........
Answer: A
Step-by-step explanation :
HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )
In 2016 the cdc estimated the mean weight of us women over the age of 20 years was 168.5 pounds with a standard deviation of 68 pounds. What is the expected mean for a sample of 150 women
The expected mean for a sample of 150 women is 168.5 pounds.
What is expected mean?Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.
The formula for expected mean is :
E ( X ) = μ = ∑ x P ( x )
Where:
x = values of the random variable X
P(x) = Corresponding probability
∑ =Sum of all products xP(x)
μ = mean
Therefore the expected mean is 168.5 pounds.
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Write the equation of the line that passes through the points (5,—9) and (-7, 7).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
Answer:
[tex]y-7=-\frac{4}{3}(x+7)[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{-9-7}{5-(-7)}=-\frac{4}{3}[/tex].
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex], so the equation is [tex]y-7=-\frac{4}{3}(x+7)[/tex].
Find the sum: (2x² + x + 3) + (3x² + 2x + 1)
A. 3x² + 5x+4
B. 5x²+3x+4
OC. 6x + 2x + 3
OD. 5x²+2x+4
Answer:
B
Step-by-step explanation:
Combine 2x^2 and 3x^2 to get 5x^2.
5x²+x+3+2x+1Combine x and 2x to get 3x.
5x²+3x+3+1Add 3 and 1 to get 4.
5x²+3x+4The correct option is B.earns $14.50 per hour. His regular hours
are 40 hours per week, and he receives
time-and-a-half overtime. Find his total pay
for a week in which he works 46 hours.
Answer: 667
Step-by-step explanation:
14.50 x 46
Question 5 (1 point), You are making your friend a triangular fabric decoration for their home. It has ripped so you need to go buy new fabric. The fabric you are buying is $3 per square foot. Using the dimensions below, how much money do you need to buy enough fabric?
Answer:
1). True
2). x = 16.4 m^2
3). A = 24, h = 4
4). A = 18.39
5). 162
Step-by-step explanation:
I took this quiz on K12 and got everything correct! Brainliest welcome! :)
4. Combine the two equations to eliminate one of the variables, and then solve for the other. (3 points: 1 for eliminating one variable, 1 for the answer, and 1 for showing your work)
The two equations combined is
3x + y = 2010x + y = 55Eliminating one variable gives
7x = 35the variables are
x = 5y = 5How to eliminate one variable in the equation formedThe equation formed is a consistent independent set of equation with two variables solved by elimination method as follows
Elimination of one of the variable
3x + y = 20 (1)
10x + y = 55 (2)
subtracting (1) from (2)
10x - 3x + y - y = 55 - 20
7x + 0 = 35
7x = 35
x = 5
substituting to find y
3x + y = 20
3 * 5 + y = 20
15 + y = 20
y = 20 - 15
y = 5
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If A and B are independent events, P(A)=0.15, and P(B)=0.77, what is P(B|A)?
The Probability of P(B│A) is 0.77
What are independent events?Independent events are those events whose occurrence is independent on any other event. For example, if we flip a coin in the air and get the outcome as tail, then again if we flip the coin but this time we get the outcome as Head, In both cases, the occurrence of both events is independent of each other. It is a type of events in probability.
If A is the event that even number will appear when a die is rolled and B is when 4 or 6 appears
P(A)= 3/6 = 1/2 and P(B) = 2/6 = 1/3
Also A and B is the event ‘the number appearing is even and a multiple of 4 or 6 so that
P(A ∩ B) = 1/6
P(B│A) = P(A ∩ B)/ P(A)
= 1/6 /1/2= 1/3 = P(B)
Therefore P(B│A) = P(B)
if A= 0.15 and P(B)= 0.77
P(B│A) = 0.77
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PLEASE SOMEONE HELP ME GIVING BRAINLIEST!!!
Answer:
23/5 > (sqrt(18)
Step-by-step explanation:
there are many ways you could go about this,
I subtracted (sqrt(18)) from (23/5) and because the answer i got was greater than 0, 23/5 must be bigger than sqrt18
What is the value of x?
The required value of x is 3 in the given equilateral triangle.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
The triangle given in the figure is an equilateral triangle.
We know that all sides are equal in the equilateral triangle.
As per the given figure,
side AB = side AC
6x - 3 = 3x + 6
6x - 3x = 6 + 3
Apply the arithmetic operation,
3x = 9
x = 9/3
x = 3
Therefore, the required value of x is 3 in the given equilateral triangle.
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Translate the sentence into an equation.
The square of a number is equal to the square root of that number.
The equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].
According to the question,
We have the following information:
The square of a number is equal to the square root of that number.
Now, let's take this number to be x.
Now, square of this number will be [tex]x^{2}[/tex] and the square root of this number will be [tex]\sqrt{x}[/tex].
Now, according to the sentence, we will have the following expression:
[tex]x^{2} =\sqrt{x}[/tex]
Hence, the equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].
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Can someone please help me , thank you :)!
Answer:
a )
[tex]6 ( ? ) = 27[/tex]
b )
? = The amount of rice in each container.
So, 1 container = ( ? ) ounce.
6 containers have = 6 x ( ? ) ounces.
We know that 6 containers have 27 ounces so...
[tex]6 ( ? ) = 27[/tex]
[tex]? = \frac{27}{6}[/tex]
[tex]? = 4.5[/tex]
Final Answer: 4.5 ounces in each container
Hope this helps! :)
if x represents the number of questions on test, analyze the meaning of each expression x+4
The meaning of the expression x + 4 as required in the task content is; "four more than the number of questions on test".
Determining word phrases from algebraic expressions.It follows from the task content that the word phrase which best represent the algebraic expression; x + 4 is to be determined.
Given; x = the number of questions on test.
It therefore follows that the algebraic expression x + 4 can be interpreted as; "four more than the number of questions on test".
Hence, the meaning of the expression is; "four more than the number of questions on test".
PS: Just like word phrases can be accurately represented by algebraic expressions, the latter can be represented by the former too.
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