Answer:
2/5*3/7= 6/35
Step-by-step explanation:
Convert 63°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. 5 C== (F-32) F=-6 +32 5 63 PF - I c
The given temperature is 63 F
The formula for convert temperature into Degree C from Degree F.
[tex]C=\frac{5}{9}(F-32)[/tex]Substitute all the value in the above equation.
[tex]\begin{gathered} C=\frac{5}{9}(63-32) \\ C=\frac{5}{9}\times31 \\ C=17.22C \end{gathered}[/tex]The nearest tenth is 17degree C.
Match the one-to-one functions with their inverse functions.
Matching the following function
What is a Function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The function of f^(-1)(x) = 5x is:
f(x)= x / 5
The function of f^(-1)(x) = x^3 / 2 is:
f(x)=3√2x
The function of f^(-1)(x) = x+10 is:
x - 10
The function of f^(-1)(x) = 3(x + 17) / 2 is:
(2x / 3) - 17
Hence, These are the Match of one-to-one functions with their inverse functions.
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graph triangle JKL with vertices j(2,3), k(-2,1), L(-1,5) and its image after the glide reflection: x-axis
Check the picture below.
What is the simplified form: (8m + 1)^2
Answer
(8m + 1)^2 = (8m + 1)² = 64m² + 16m + 1
Explanation
The question simply wants us to simplify the expression
(8m + 1)^2
= (8m + 1)²
= (8m + 1) (8m + 1)
= 8m (8m + 1) + 1 (8m + 1)
= 64m² + 8m + 8m + 1
= 64m² + 16m + 1
Hope this Helps!!!
An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 45% probability of winning the first contract. If they win the first contract, the probability of winning the second is 75%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 52%.
1. The probability that they win both contract will be 23.4%.
How to calculate the probability?It should be noted that probability simply means the likelihood that an event will occur.
The probability of winning the contract will be:
= Probability of A winning × Probability of B winning
= 45% × 52%
= 0.45 × 0.52
= 0.234
= 23.4%
The probability is 23.4%
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The area of the triangle below is40 square meters. What is the length of the base?Express your answer as a fraction in simplest form.
Given the area of the triangle:
[tex]A=\frac{3}{40}m^2[/tex]You can identify in the figure provided in the exercise that the height of the triangle is:
[tex]h=\frac{1}{5}m[/tex]The area of a triangle can be calculated using this formula:
[tex]A=\frac{bh}{2}[/tex]Where "A" is the area, "b" is the base, and "h" is the height.
If you solve for "b", you obtain this formula:
[tex]\begin{gathered} 2A=bh \\ \\ b=\frac{2A}{h} \end{gathered}[/tex]Therefore, knowing the Area and the height of the triangle, you can substitute them into the formula and then evaluate, in order to find the length of its base:
[tex]b=\frac{(2)(\frac{3}{40})}{\frac{1}{5}}[/tex][tex]b=\frac{\frac{6}{40}^{}}{\frac{1}{5}}[/tex][tex]b=\frac{6\cdot5}{40\cdot1}[/tex][tex]b=\frac{30}{40}[/tex][tex]b=\frac{3}{4}m[/tex]Hence, the answer is:
[tex]b=\frac{3}{4}m[/tex]Bea is asked to graph this system of equations: 8x - 6y= 3 -3y + 4x = 4 How many times will the lines intersect?
Given the system of equations:
8x - 6y = 3
-3y + 4x = 4
To find how many times the lines will intersect. let's solve the system of equation using substitution method.
8x - 6y = 3 ........................................1
-3y + 4x = 4 ......................................2
From equation 1, make x the subject:
8x - 6y = 3
8x = 3 + 6y
[tex]\begin{gathered} x=\frac{3}{8}+\frac{6}{8}y \\ \\ x=\frac{3}{8}+\frac{3}{4}y \end{gathered}[/tex][tex]\text{Substitute (}\frac{3}{8}+\frac{3}{4}y)\text{ for x in equation 2}[/tex]We have:
[tex]\begin{gathered} -3y+4(\frac{3}{8}+\frac{3}{4}y)=4 \\ \\ -3y+\frac{3}{2}+3y=4 \\ \\ \end{gathered}[/tex]Multiply through by 2 to eliminate the fraction:
[tex]\begin{gathered} -3y(2)+\frac{3}{2}(2)+3y(2)=4(2) \\ \\ -6y+3+6y=8 \end{gathered}[/tex][tex]\begin{gathered} -6y+6y=8-3 \\ \\ 0=5 \end{gathered}[/tex]Since we have 0 = 5, it means the system of equations has no solution.
Therefore, the lines will not intersect, because this system has no solution.
ANSWER:
A. The lines will not intersect, because this system has no solution.
For each system to the best description of a solution if applicable give the solution
System A
[tex]\begin{gathered} x-4y=4 \\ -x+4y+4=0 \end{gathered}[/tex]solve the first equation for x
[tex]x=4+4y[/tex]replace in the second equation
[tex]\begin{gathered} -(4+4y)+4y+4=0 \\ -4-4y+4y+4=0 \\ 0=0 \end{gathered}[/tex]The system has infinitely many solutions, They must satisfy the following equation
[tex]\begin{gathered} x-4y=4 \\ -4y=4-x \\ y=\frac{4}{-4}-\frac{x}{-4} \\ y=\frac{x}{4}-1 \end{gathered}[/tex]System B
[tex]\begin{gathered} x-2y=6 \\ -x+2y=6 \end{gathered}[/tex]solve for x for the first equation
[tex]x=6+2y[/tex]replace in the second equation
[tex]\begin{gathered} -(6+2y)+2y=6 \\ -6-2y+2y=6 \\ -6=6 \end{gathered}[/tex]The system has no solution.
variables review find w if 67.1=29.7-0.2w
Given the following equation:
[tex]67.1=29.7-0.2w[/tex]You need to solve for the variable "w" in order to find its value. To do this, you can follow the steps shown below:
1. You can apply the Subtraction property of equality by subtracting 29.7 from both sides of the equation. Then:
[tex]\begin{gathered} 67.1-(29.7)=29.7-0.2w-(29.7) \\ 37.4=-0.2w \end{gathered}[/tex]2. Finally, you need to apply the Division property of equality by dividing both sides of the equation by -0.2. Then, you get:
[tex]\begin{gathered} \frac{37.4}{-0.2}=\frac{-0.2w}{-0.2} \\ \\ w=-187 \end{gathered}[/tex]The answer is:
[tex]w=-187[/tex]URGENT!!) Which of the following served as the primary route for transporting cotton to Georgia's only sea port? (5 points)
a
The Savannah River
b
The Chattahoochee River
c
The Oconee River
d
The Suwanee River
Answer:
Correct answer:
a. The Savannah River
Lashonda, Josh, and Brian sent a total of 90 text messages during the weekend, Lashonda sent 10 more messages than Josh. Brian sent 2 times as manymessages as Josh. How many messages did they each send?Number of text messages Lashonda sent:Number of text messages Josh sent:Number of text messages Brian sent:
Defining:
Number of messages of Lashonda = L
Number of messages of Josh = J
Number of messages of Brian = B
We know that:
L+J+B=90 (Equation 1)
We also know:
L = J+10 (Equation 2)
B=2J (Equation 3)
Now, we can substitue the values for L and B in the first equation
L+J+B=90
J+10 + J + 2J = 90
4J=90-10
4J=80
J=80/4
J=20
Since you found how many messages Josh sent, we can return to Equation 2 and 3:
L = J+10
L = 20 + 10
L = 30
B=2J
B=2*20
B=40
ANSWER:
Number of text messages Lashonda sent: 30
Number of text messages Josh sent: 20
Number of text messages Brian sent: 40
Part II: Constructed Response15. An amusement park has two carousels. The first carousel has a circularplatform with a diameter of 13 meters, and the second carousel has acircular platform with a diameter of 19 meters. How much larger is thearea of the larger carousel's platform than the area of the smallercarousels platform? Show your work, using 3.14 for r.151st find Area of First Carousel:16. Next find Area of Second Carousel:127.6.417. What is the difference between the two areas?
- Area of First Carousel:
diameter = 13 m
[tex]\text{Area}=\pi\cdot\frac{d^2}{4}=(3.14)\cdot\frac{(13)^2}{4}=3.14\cdot\frac{169}{4}=\frac{530.66}{4}=132.7m^2[/tex]- Area of Second Carousel:
diameter = 19 m
[tex]\text{Area}=(3.14)\cdot\frac{(19)^2}{4}=3.14\cdot\frac{361}{4}=\frac{1133.54}{4}=283.4m^2[/tex]- The difference between the two areas is:
[tex]283.4-132.7=150.7m^2[/tex]Answer:
The platform area of the larger carousel is 150.7 m^2 larger than the platform area of the smaller carousel.
Help mee pleasee!!
thank you <3
...................
"An orchestra of 120 players take 70 minutes to play Beethoven's 9th symphony," "How long would it take for 60 players to play the symphony?"Answer the question an explain*
We have that in 70 minutes 120 players of an orchestra play Beethoven's 9th symphony because it always lasts 70 minutes.
The lenght of a musical piece does not depend in the number of musicians playing it. The orchestra could have 2 violinists more or less and they still will play the same 70 minutes musical piece.
Then, an orchestra of 60 players would take the same 70 minutes to play Beethoven's 9th symphony.
Answer: 70 minutes(3^9)/(3^-9)simpilfy. write your answer using a positive exponent
Simplifying:
[tex]\frac{3^9}{3^{-9}}\rightarrow3^{9-(-9)}\rightarrow3^{9+9}\rightarrow3^{18}[/tex]What is the approximate area of a clock face with a diameter of eight inches?
The area formula of a circle is :
[tex]A=\frac{1}{4}\pi D^2[/tex]From the problem, the diameter is 8 inches.
The area will be :
[tex]\begin{gathered} A=\frac{1}{4}\pi(8)^2 \\ A=50.27 \end{gathered}[/tex]The answer is 50.27 in^2
Identify the property used in each step of solving the inequality 7x+4 <46,
Step
7x+4 <46
7x <42
x <6
Answer:
1) Given
2) Subtraction Property of Inequalities
3) Division Property of Inequalities
For the following exercises, evaluate the function f at the indicated values.
a. f(-3) b. f(2) c. f(-a) d. -f(a)
4. f(x)=2x-5
5. f(x)=−5x²+2x−1
6. f(x)=x-1-x+1
After we evaluate the function f at the indicated values the results are
a. (4) −11, (5) −52, (6) 0
b. (4) -1, (5) −17, (6) -5
c. (4) −2a−5, (5) −5a² −2a−1, (6) −3+a
d. (4) −2a+5, (5) 5a² −2a+1, (6) 3+a
What is function?A relation in which there is only one possible pairing of each x and each y is called a function. It should be noted that while the reverse is true, the same y can be paired with different x. Vertical and horizontal lines are the only types of linear equations that are not functions.
Lets evaluate the function a. f(-3)
4. f(-3) = 2(-3)-5
= −11
5. f(-3) = −5(-3)²+2(-3)−1
= −52
6. f(-3) = -3-1-(-3)+1
= 0
Lets evaluate the function b. f(2)
4. f(2) = 2(2)-5
= −1
5. f(2) = −5(2)²+2(2)−1
= −17
6. f(2) = -3-1-(2)+1
= −5
Lets evaluate the function c. f(-a)
4. f(-a) = 2(-a)-5
= −2a−5
5. f(-a) = −5(-a)²+2(-a)−1
= −5a² −2a−1
6. f(-a) = -3-1-(-a)+1
= −3+a
Lets evaluate the function d. -f(a)
4. -f(a) = -(2(a)-5)
= −2a+5
5. -f(a) = -(−5(a)²+2(a)−1)
= 5a² −2a+1
6. -f(a) = -(-3-1-(a)+1)
= 3+a
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I need help with my math
Answer:
Sure
Step-by-step explanation:
Let me know what you want by making me brainliest
14. Sort each number of miles and number of hours traveled into the appropriate bin to identify the rate in miles per hour. 6.NS.2 718 miles in 5.95 hours 45.8 miles In 4 hours 2,865 miles in 24.8 hours 419.72 miles in 80.6 hours 935.47 miles in 22.75 hours Las Toan 10 MIO por Hour Between 10 and 99 Miles per Hour Greater Than 100 Miles per Hour
we have
Find the unit rate in each case
so
718/5.95=120.67 miles per hour ---------> greater than 100 miles per hour
45.8/4=11.45 miles per hour ------> between 10 and 96 miles per hour
2,865/24.8=115.52 miles per hour -------> greater than 100 miles per hour
419.72/80.6=5.21 miles per hour ------------> less than 10 miles per hour
935.47/22.75=41.12 miles per hour ------> between 10 and 96 miles per hour
Marco bought 12 roses for
$48. What was the original
cost of EACH rose before
the discount? Set up an
equation and solve to
answer this question
Super Saver
DEALS! Get $2
off each rose
when you buy 12
or more roses
Marco bought 12 roses for $48. Each rose was originally $4 before the discount, and Super Saver Get $2 off each rose when you buy 12 or more roses each rose is $6.
How to calculate discount?The discount formula is as follows: Discount = Marked Price - Selling Price. OR. Formula for Discount Percentage = Marked Price Discount Rate A 10% discount can be calculated in two steps: Step 1 is to convert your percentage to a decimal using the formula 10 / 100 = 0.1. As a decimal, 10% equals 0.1. Step 2 is to multiply your original price by the decimal you chose. The sweaters were originally priced at $80. The store would like to offer a 15% discount on the sweaters. The company converts 15% to the decimal 0.15 to calculate the discount. The result is a figure of $12 after multiplying 0.15 by the original price of $80.Therefore,
Marco bought 12 roses for $48. Each rose was originally $4 before the discount.
∴ 48/12 = $4 and,
Super Saver Get $2 off each rose when you buy 12 or more roses
each rose is $6.
∴ 12/2 = $6
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Hi, can you help me with this exercise please, Find the value of x. Round lengths of segments to the nearest tenth and angle measures to the nearest degree.
From the given figure , we will use the Sine function in order to find segment x .
Sin 70 ° = opposite /hypotaneus
Sin 70 ° =x /7
∴x = 7* Sin 70°
x = 6.5778
x ≈6.6 ...( rounded to the nearest 10 )
Write the equation of the line with the points (0, 2) and (4, 10) in standard form.
By definition, the of a line written in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
You know that this line passes through these points:
[tex](0,2);(4,10)[/tex]By definition, the value of "x" is zero when the line intersects the y-axis. Then, you can identify that, in this case:
[tex]b=2[/tex]Now you can substitute the value of "b" and the coordinates of the second point into the following equation and solve for "m":
[tex]y=mx+b[/tex]Then, the slope of the line is:
[tex]\begin{gathered} 10=m(4)+2 \\ 10-2=4m \\ 8=4m \\ \\ \frac{8}{4}=m \\ \\ m=2 \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept form is:
[tex]y=2x+2[/tex]To write it in Standard form, you can follow these steps:
- Subtract 2 from both sides of the equation:
[tex]\begin{gathered} y-(2)=2x+2-(2) \\ y-2=2x \\ \end{gathered}[/tex]- Subtract "y" from both sides of the equation:
[tex]\begin{gathered} y-2-(y)=2x-(y) \\ -2=2x-y \\ 2x-y=-2 \end{gathered}[/tex]The answer is:
[tex]2x-y=-2[/tex]Answer:
2x-y =-2
Step-by-step explanation:
To find the equation of the line in standard form, first, we need to find the slope
m = ( y2-y1)/(x2-x1)
m = (10-2)/(4-0)
= 8/4 = 2
Then we can use the slope intercept form
y = mx+b where m is the slope and y is the y-intercept
y = 2x +b
Using the y-intercept ( 0,2)
y = 2x +2
The standard form is Ax +By =C where A is a positive integer and B is an integer
Subtract 2x from each side
-2x +y = 2
Multiply each side by -1
2x-y =-2
A company has determined that the demand function for a certain couch is given by
= 2700 − 0.75, where p is the price per couch, and x is the number of couches sold. The fixed costs associated with producing a line of couches is $760,000, and each couch costs $360 to make. Determine how many couches should be manufactured and sold in order to maximize profit. Start by finding functions to represent the revenue and the total cost, then find a function for profit
The number of couches manufactured and sold in order to maximise the profit is 1560.
The demand function will be
p = 2700 - 0.75x
Here p = price per couch and x = number of couch
Total Fixed cost = $760000
Variable cost per couch = $360
Total cost = Fixed cost + variable cost
T(x) = 760000 + 360x
Revenue function will be
R(x) = Px
(2700 - 0.75x)x
2700x - 0.75x²
Since profit function = Pr(x)
Pr(x) = R(x) - T(x)
= 2700x - 0.75x² -760000 -360x
- 0.75x² + 2700x - 360x - 760000
For maximum profit
[tex]\frac{d}{dx}(Pr(x)) = 0[/tex]
[tex]\frac{d}{dx}[-0.75x^{2} + 2340x -760000 ] = 0[/tex]
-1.5x + 2340 = 0
x = 2340/1.5
x = 1560
The couches sold for maximum profit = 1560
Therefore, the number of couches manufactured and sold in order to maximise the profit is 1560.
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How do I solve the missing verticals angles for L2 and L3?
The vertical angle theorem states that two opposite angles that are formed when two lines intersect each other are always equal, graphically this looks like this:
Then, if we apply this theorem to the figure shown we can say that
[tex]\begin{gathered} L1=L3 \\ L2=L4 \end{gathered}[/tex]This means that:
[tex]\begin{gathered} L2=110.6 \\ L3=69.4 \end{gathered}[/tex]Consider the functions f(x) and g(x). The function f(x)=2x-5 and g(x)= -f(x+1)+3. A. Describe the three transformations that are performed on f(x) to create g(x).1.2.3.B. Sketch a graph of g(x):
First we have to take a look at the expression f(x + 1). This represents an horizontal translation. So this is the first transformation:
1. Horizontal translation
Now we can see that we have to multiply f(x + 1) by -1. This represents a reflexion on the y-axis
2. Reflection on y-axis
Finally we can see that -f(x + 1) is added by 3 units. This represents a vertical translation:
3. Vertical translation
Answer:
1. Horizontal translation
2. Reflection on y-axis
3. Vertical translation
Now let's see the final function:
f(x) = 2x - 5
f(x+1) = 2(x + 1) - 5
f(x+1) = 2x + 2 - 5
f(x+1) = 2x - 3
g(x) = -2x + 3 + 3
g(x) = -2x + 6
So let's plot f and g on the same reference system:
A linear function is shown on the graph
6
What is the domain of the function?
O(x10≤x≤4)
O(x10
Oy 12sy≤6)
0012
Question 1 (Answered)
MATHEMATICALLY we say
[tex]0 \leqslant x \leqslant 4[/tex]
THAT IS THE DOMAIN OF THE GRAPH
THAT IS THE DOMAIN OF THE GRAPHOPTION A IS THE ANSWER.
What is the slope of the line passing through the points (0, 5) and (4,2) ^ prime
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ -3 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{ 3 }{ 4 } \end{array}}[/tex]
Solve the word problem. Show all the steps.
Two numbers add to 39. One number is 9 less than 7 times the other. What are the numbers?
The numbers represented by the word problems are 33 and 6
How to determine the solution to the word problem?The statements in the question are:
Two numbers add to 39. One number is 9 less than 7 times the other.Let the numbers in the expressions be x and y
So, we have
x + y = 39
x = 7y - 9
Substitute x = 7y - 9 in the equation x + y = 39
So, we have
7y - 9 + y = 39
Evaluate the like terms
8y = 48
Divide both sides by y
y = 6
Substitute y = 6 in x + y = 39
x + 6 = 39
Evaluate the like terms
So, we have
x = 33
Hence, the numbers are 33 and 6
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Find the range and mean of each data set. Use your results to compare the two data sets.Set A:Set B:2 10 8 19 2314 16 15 17 16
Range of a Data Set :
The range of a set of data is the difference between the highest and lowest values in the set
MEAN :
The mean is the mathematical average of a set of two or more numbers
Set A: 2, 10, 8, 19, 23
Arrange the data of set A in ascending order;
Set A : 2, 8, 10, 19, 23
For range; the highest term is 23, lowers term is 2
Range = highest - lowest
Range = 23 - 2
Range = 21
for Mean; the sum of all entries divided by the total number of entries in data set.
In data A, total number of entries are : 5
[tex]\begin{gathered} \text{ Mean = }\frac{2+8+10+19+23}{5} \\ \text{Mean}=\frac{62}{5} \\ \text{Mean}=12.4 \end{gathered}[/tex]Thus, mean of set A is 12.4
Now, for set B;
Set B : 14 16 15 17 16
Arrange the elements of set B in the ascending order;
Set B : 14, 15, 16, 16, 17
For range; the highest term is 17, lowers term is 14
Range = highest - lowest
Range = 17-14
Range = 3
Thus, range of set B is 3
for mean of set B;
The sum of all entries divided by the total number of entries in data set.
In data B, total number of entries are : 5
[tex]\begin{gathered} \text{ Mean = }\frac{14+16+15+17+16}{5} \\ \text{Mean}=\frac{78}{5} \\ \text{Mean}=15.6 \end{gathered}[/tex]Thus, the mean for set B is 15.6
Answer : The mean of set A is 12.4 and range is 21
The mean of set B is 15.6 and range is 3
