Consider the given expression,
[tex]P=\frac{4}{7}\times\frac{1}{2}[/tex]The product of fractions is obtained in the form of a fraction whose numberator is the product of numerators of fractions, and the denominator of the product is the product of denominators of the given fractions,
[tex]\begin{gathered} P=\frac{4\times1}{7\times2} \\ P=\frac{4}{14} \end{gathered}[/tex]Thus, the product of the given fractions is 4/14 .
Solve each system of equations algebraically.[tex]y = {x}^{2} + 4 \\ y = 2x + 7[/tex]
From the problem, we two equations :
[tex]\begin{gathered} y=x^2+4 \\ y=2x+7 \end{gathered}[/tex]Since both equation are defined as y in terms of x, we can equate both equations.
[tex]\begin{gathered} y=y \\ x^2+4=2x+7^{} \end{gathered}[/tex]Simplify and solve for x :
[tex]\begin{gathered} x^2+4=2x+7 \\ x^2-2x+4-7=0 \\ x^2-2x-3=0 \end{gathered}[/tex]Factor completely :
[tex]\begin{gathered} x^2-2x-3=0 \\ (x-3)(x+1)=0 \end{gathered}[/tex]Equate both factors to 0 then solve for x :
x - 3 = 0
x = 3
x + 1 = 0
x = -1
We have two values of x, x = 3 and -1
Substitute x = 3 and -1 to any of the equation, let's say equation 2 :
For x = 3
y = 2x + 7
y = 2(3) + 7
y = 6 + 7
y = 13
One solution is (3, 13)
For x = -1
y = 2x + 7
y = 2(-1) + 7
y = -2 + 7
y = 5
The other solution is (-1, 5)
The answers are (3, 13) and (-1, 5)
You are looking for summer work to help pay for college expenses. Your neighbor is interested in hiring you to do yard work and other odd jobs. You tell them that you can start right away and will work all day July 1 for 3 cents. This gets your neighbor's attention, but they is wondering if there is a catch. You tell them that you will work July 2 for 9 cents, July 3 for 27 cents, July 4 for 81 cents, and so on for every day in the month of July. Which equation will help you determine how much money you will make in July?
Answer:
y=3^x
Explanation:
The expected payments (in cents) beginning from July 1 are given below:
[tex]3,9,27,81,\cdots[/tex]Observing the payments for each subsequent day, we see that the payment for the previous day was multiplied by 3.
We can rewrite the payment as a power of 3 as follows:
[tex]3^1,3^2,3^3,3^4,\cdots[/tex]Therefore, the equation will help you determine how much money you will make in July will be:
[tex]y=3^x[/tex]The first option is correct.
6. sin D - Ог F 25 ot E 7. cos F. 24 8. sin F Nodule 13
In the given triangle :
FD = 25, FE = 7, DE = 24
SinD
From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,
So, the SinD is express as :
[tex]\begin{gathered} \sin D=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin D=\frac{FE}{DF} \\ \sin D=\frac{7}{25} \end{gathered}[/tex]sin D = 7/25
cos F
From the trignometric ratio of cos : It expresses as the ratio of measurement of the side adjacent to the angle and to the hypotenuse of the triangle
So, the Cos F is express as :
[tex]\begin{gathered} \cos F=\frac{Adjacent\text{ side}}{Hypotenuse} \\ \cos F=\frac{FE}{DF} \\ \cos F=\frac{7}{25} \end{gathered}[/tex]cos F = 7/25
Sin F
From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,
so, Sin F is express as :
[tex]\begin{gathered} \sin F=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin F=\frac{DE}{DF} \\ \sin F=\frac{24}{25} \end{gathered}[/tex]sin F = 24/25
Answer :
sin D = 7/25
cos F = 7/25
sin F = 24/25
use the figure to the right to find the value of PT
the figure show, the length between P and T and the length between T and Q, are equal.
so we can say PT=TQ
PT= 3x+2 and TQ=5x-6
so we can replace:
3x+2=5x-6
now we solve
2+6=5x-3x
8=2x
8/2=x=4
and finally, to find PT we replace x by 4
PT=3*4+2=14
So the answer is: PT=14
Which of the following are solutions to the inequality below? Select all that apply.
Step-by-step explanation:
1.12+8×10<66
12+80<66
92<66
2.12+8×3<66
12+24<66
36<66
3.12+8×8<66
12+64<66
76<66
4.12+8×4<66
12+32<66
44<66
therfore the answer is 2 and 4
Over the next 10 years, town A is expecting to gain 1000 people each year. During the same time period, the population of town B is expected to increase by 5% each year. Both town A and town B currently have populations of 10,000 people. The table below shows the expected population of each town for the next three years.Which number of years is the best approximation of the time until town A and town B once again have the same population?
From the given figure we can see
The population in town A is increased by a constant rate because
[tex]\begin{gathered} 11000-10000=1000 \\ 12000-11000=1000 \\ 13000-12000=1000 \end{gathered}[/tex]Since the difference between every 2 consecutive terms is the same, then
The rate of increase of population is constant and = 1000 people per year
The form of the linear equation is
[tex]y=mx+b[/tex]m = the rate of change
b is the initial amount
Then from the information given in the table
m = 1000
b = 10,000
Then the equation of town A is
[tex]y=1000t+10000[/tex]Fro town B
[tex]\begin{gathered} R=\frac{10500}{10000}=1.05 \\ R=\frac{11025}{10500}=1.05 \\ R=\frac{11576}{11025}=1.05 \end{gathered}[/tex]Then the rate of increase of town by is exponentially
The form of the exponential equation is
[tex]y=a(R)^t[/tex]a is the initial amount
R is the factor of growth
t is the time
Since R = 1.05
Since a = 10000, then
The equation of the population of town B is
[tex]y=10000(1.05)^t[/tex]We need to find t which makes the population equal in A and B
Then we will equate the right sides of both equations
[tex]10000+1000t=10000(1.05)^t[/tex]Let us use t = 4, 5, 6, .... until the 2 sides become equal
[tex]\begin{gathered} 10000+1000(4)=14000 \\ 10000(1.05)^4=12155 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(5)=15000 \\ 10000(1.05)^5=12763 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(6)=16000 \\ 1000(1.05)^6=13400 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(30)=40000 \\ 10000(1.05)^{30}=43219 \end{gathered}[/tex]Since 43219 approximated to ten thousand will be 40000, then
A and B will have the same amount of population in the year 30
The answer is year 30
3 hours 6 minutes 45 seconds Plus 8 hours 55 minutes 20 seconds
12h 2 minutes and 5 seconds
1) Adding 3 hours 6 minutes and 45 seconds to 8 hours 55 minutes and 20 seconds we can write like this:
2) Every time we hit 60'' (seconds) we add to its neighbor then we can find the following sum.
1h ----60'
1 minute ----60''
3) Then the sum of those is equal to 12h 2 minutes and 5 seconds
In ACDE, m/C= (5x+18), m/D= (3x+2), and m/B= (2+16)°.
Angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.CDE provides the following: 3. angles
m<C=(5x+18),m<D=(3x+2), andm<E=(x+16)degree.The total of the angles in a triangle is 180 degrees, so:
"mC + mD + mE = 180°"(5x+18)° + (3x+2)° + (x+16)° = 180°5x + 18 + 3x + 2 + x + 16 = 180°5x + 3x + x + 18 + 2 + 16 = 180°9x +36= 180°From both sides, deduct 36 as follows:
9x + 36 - 36 = 180° - 36°9x = 144°x = 144°/9x = 16From the aforementioned query, we are requested to determine:
angular D (m<D)Hence:
m∠D=(3x+2)°m∠D=( 3 × 16 + 2)°m∠D=(48 + 2)°m∠D= 50°Therefore, angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°To learn more about angles, refer to:
brainly.com/question/25716982
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How many times in the parabola does a line intersect?
The line can intersect the parabola at one or two points.
See the example below.
The black line intersects the parabola at (1, -1)
The blue line intersects the parabola at two points: (0, 0) and (4, 8).
What’s the correct answer answer asap for brainlist please
Answer:
c. you can't be feeling alive with wearing,weakness of body and mind.
A line passes through the point −6, 3 and has a slope of 32 .Write an equation in slope-intercept form for this line.
The equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195.
What is the slope - intercept form of the equation of a straight line?
The slope - intercept form of the equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that passes through the point (−6, 3) and has a slope of 32.
We know that the slope - intercept form can be written as -
y = mx + c
Now, the slope of the line = [m] = 32
Since, the line passes through the point (-6, 3), we can write -
3 = 32 x -6 + c
3 = -192 + c
c = 3 + 192
c = 195
So, the equation of the straight line that passes through the point (-6, 3) will be -
y = 32x + 195
Therefore, the equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195
To solve more questions on straight line, visit the link below-
https://brainly.com/question/27730503
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As the table shows, projections indicate that the percent of adults with diabetes could dramatically increase.Answer parts a. through c.c. In what year does this model predict the percent to be 27.96%(round to the closest year)
b. You have to consider year 2000 as the initial year, i.e. as x=0.
To predict the percent of adults with diabetes in 2014, first, you have to calculate the difference between this year and the initial year to determine which value of x you need to use:
[tex]x=2014-2000=\text{ }14[/tex]The value of x you have to use is x=14
Replace this value into the linear model calculated in item a to predict the percentage of adults with diabetes (y)
[tex]\begin{gathered} y=0.508x+10.692 \\ y=0.508\cdot14+10.692 \\ y=7.112+10.692 \\ y=17.804 \end{gathered}[/tex]In the year 2014, the predicted percentage of adults with diabetes is 17.8%
c. You have to determine the year in which the model predicts the percent to be 27.96%.
To determine this year, you have to equal the linear model to 27.96% and calculate for x:
[tex]\begin{gathered} y=0.508x+10.692 \\ 27.96=0.508x+10.692 \end{gathered}[/tex]-Subtract 10.692 from both sides of the equal sign
[tex]\begin{gathered} 27.96-10.692=0.508x+10.692-10.692 \\ 17.268=0.508x \end{gathered}[/tex]-Divide both sides by 0.508
[tex]\begin{gathered} \frac{17.268}{0.508}=\frac{0.508x}{0.508} \\ 33.99=x \\ x\approx34 \end{gathered}[/tex]Next, add x=34 to the initial year:
[tex]2000+34=2034[/tex]The model predicts the percentage to be 27.96% for the year 2034
Three-inch pieces are repeatedly cut from a 42-inch string. The length of the string after x cuts is given by y = 42 – 3x. Find and interpret the x- and y-intercepts.
Answer:
y-intercept: 42
x-intercept: 14
Step-by-step explanation:
The y-intercept can be found with the given equation:
y = 42 - 3x
Either Let x = 0 to find the y-intercept. OR,
rearrange the equation to y=mx+b to see the y-intercept, which is b in the equation.
y = 3(0) + 42
y = 42
The y-intercept is 42 and this means that the original, uncut length of the string (zero cuts) is 42.
To find the x-intercept, let y = 0.
y = 42 - 3x
0 = 42 - 3x
Add 3x to both sides.
3x = 42
Divide by 3.
x = 42/3
x = 14
An x-intercept of 14, means that at 14 cuts there will be no more string left. The length of the string is now 0.
B and Care sets of real numbers defined as follows.
Answer:
[tex]\begin{gathered} B\cap C=\phi \\ (-\infty,\text{ 1)}\cup\lbrack9,\infty) \end{gathered}[/tex]Step-by-step explanation:
Solve this situation with the help of the number line, if B and C are sets of real numbers defined as follow:
The intersection is an interval that lies within all of the given intervals. If no such intersection exists then the set is empty.
In this case, for the intersection between B and C:
[tex]\begin{gathered} B\cap C=\phi \\ \end{gathered}[/tex]For the union between B and C:
[tex](-\infty,\text{ 1)}\cup\lbrack9,\infty)[/tex]How do the graphs of transformations compared to the graph of the parent function. Need the answer to this
• A ,Reflection
,• A ,Vertical Shift 4 units down
1) Considering the parent function, i.e. the simplest form of a family of functions, in this case, to be:
[tex]f(x)=x^4[/tex]2) Then we can state that this transformed function:
[tex]g(x)=-x^4-8[/tex]We can see the following transformations:
• A ,Reflection,, pointed out by the negative coefficient
,• A ,Vertical Shift 4 units down
As we can see below, to better grasp it:
determine whether or not each spaceship trip below has the same speed as Saiges spaceship
1) Since Saige's spaceship makes 588 km in 60 seconds we can find its velocity:
[tex]\begin{gathered} V=\frac{d}{t} \\ V=\frac{588}{60}=\frac{49}{5}\text{ =9.8 km /s} \\ \\ V_2=\frac{441}{45}=\frac{49}{5} \\ V_3=\frac{215}{25}=\frac{43}{5} \\ V_4=\frac{649}{110}=\frac{59}{10} \end{gathered}[/tex]2) After simplifying we can state:
441/45 = has the same speed as Saige's spaceship
215/25 = does not have the same speed as Saige's space
649/110 =does not have the same speed as Saige's space
please show work on how to get the points we graph
Answer:
Graphing the inequalities, we have;
Explanation:
Given the system of quadratic inequalities;
[tex]\begin{cases}y<-x^2-x+8 \\ y>x^2+2\end{cases}[/tex]Graphing the quadratic inequalities;
for the first quadratic inequality;
[tex]\begin{gathered} y<-x^2-x+8 \\ at\text{ x=0} \\ y<8 \\ (0,8) \\ at\text{ x=-0.5} \\ y<-(-0.5)^2-(-0.5)+8 \\ y<8.25 \\ (-0.5,8.25) \\ at\text{ x=-2} \\ y<-(-2)^2-(-2)+8 \\ y<-4+2+8 \\ y<6 \\ (-2,6) \\ at\text{ x=}2 \\ y<-(2)^2-(2)+8 \\ y<-4^{}-2+8 \\ y<2 \\ (2,2) \end{gathered}[/tex]For the second quadratic inequality;
[tex]\begin{gathered} y>x^2+2 \\ at\text{ x=0} \\ y>2 \\ at\text{ x=2} \\ y>(2)^2+2 \\ y>6 \\ (2,6) \\ at\text{ x=-2} \\ y>(-2)^2+2 \\ y>6 \\ (-2,6) \end{gathered}[/tex]Graphing the two inequalities using the points derived above.
Note that both inequalities would be dashed lines because of the inequality sign, and the shaded part will be according to the sign.
Graphing the inequalities, we have;
provide evidence that this function is not one to one. explain how your evidence supports that g(x) is not one to one
we have the function
g(x)=(x/3)+2 ---------> interval (-infinite, 1)
g(x)=4x-2 ------> interval [1, infinite)
the given function is not one-to -one function, because don't pass the Horizontal Line Test.
Example
For the horizontal line
y=2
we have the values of
x=0 ---------> g(x)=(x/3)+2
and
x=1 -----------> g(x)=4x-2
that means
two elements in the domain of g(x) correspond to the same element in the range of g(x)
therefore
the function is not one to oneto rent a van a moving company charges $40.00 plus $0.50per miles
The problem talks about the cost for renting a van, which can be calculated adding $40.00 plus $0.50 for each mile.
The problem asks to wirte an explicit equation in slope-intercept form which can represent the cost of renting a van depending on the amount of miles. Then, the problem asks to find the cost if you drove 250 miles.
Write the following phrase as a variable expression. Use x to represent “a number” The sum of a number and fourteen
we can write "the sum of a number and fourteen", given that x represents any number, like this:
[tex]x+14[/tex]I don't understand how to do this (this is a practice assessment)
Math | English | Art | Total
Boys 13 25 11 49
Girls 7 20 6 33
Total 20 45 17 82
1) Let's set a table, based on the given information:
• Since there are 20 students enrolled in Math let's place it into the Total, 20 -13 = 7
,• 82 students altogether.
,• 11 boys are in Art , 17 altogethe then 17 -11 = 6 girls
,• 20+6+7 = 20+13 = 33 girls altogether.
,• 82 -33 =49 13 +x +11 = 49 x = 49 -24=25
,• And lastly English: 20 +25 = 45
2) That's our table:
Math | English | Art | Total
Boys 13 25 11 49
Girls 7 20 6 33
Total 20 45 17 82
identify the constant of proportionality in the following questions. 1) y= 2x + 32) y= -3x - 4
Answer:
0. k=2
,1. k=-3
Explanation:
The constant of proportionality is the number that is beside the variable x in both equations.
(1)For the equation:
[tex]y=2x+3[/tex]The constant of proportionality is 2.
(2)For the equation:
[tex]y=-3x-4[/tex]The constant of proportionality is -3.
I just finished my other 2 questions and I need help with this one now, I don't understand the letters really. please help
So, c(x) = 8.25x + 1500
the marginal cost doubles so, (8.25 x) will be 2 * (8.25x )
And the fixed cost decreased by 30%
so, 1500 will be (1 - 30%) of 1500
so, (1 - 30%) of 1500 = 70% of 1500 = 0.7 * 1500 = 1050
So, k(x) = 2 * (8.25x) + 1050
K(x) = 16.5 x + 1050
Question 3 (5 points) Convert the decimal 0.929292... to a fraction. O 92 99 O 92 999 O 92 100 92 1000
Calculate the probability of winning: Roll two standard dice. You win if you get a sum of 4 or get a sum of 8. Round answer to one decimal place, for example if your answer is 0.65 enter 0.7
SOLUTION
The possible outcomes for sum of numbers when rolling two dice is shown
The total possible outcome is 36
The possible number of outcome of obtaining a 4 is 3
Therefore the probability of getting a sum of 4 is
[tex]\frac{3}{36}=\frac{1}{12}[/tex]The possible number of outcome of obtaining a 8 is 5
Therefore the probability of getting a sum of 8 is
[tex]\frac{5}{36}[/tex]Hence the probability of getting a sum 4 or a sum of 8 is
[tex]\frac{1}{12}+\frac{5}{36}[/tex]This gives
[tex]0.2[/tex]Therefore the probability of getting a sum 4 or a sum of 8 is 0.2
If the vertices of three squares are connected to form a right triangle, the sum of the areas of the two smaller squares is the same as the area of the largest square. Based on this statement and the model below, what is the area of square B? (Figure is not drawn to scale.) B 8 m 2 289 m
One square has area 289 square meters, and the other has area
[tex]8m\times8m=64m^2[/tex]Then, since the sum of the two areas of the smaller squares is equal to the area of the big square, we have
[tex]\begin{gathered} B+64m^2=289m^2 \\ B=289m^2-64m^2 \\ B=225m^2 \end{gathered}[/tex]Expected FrequencyA fair five sided spinner is spun 40 times.a) How many times would it be expectedto land on red?P(Red) = 15It would be expected to land on redItimes.1-5Hint:Set up and solve a proportion.
It can be observed that sppiner is spun 40 times. So proabaility for red colour must include 40 in denominator. The fraction 1/5 has 5 in denominator which be change to 40 by multiplication of 8 to numerator and denominator.
[tex]\frac{1}{5}\cdot\frac{8}{8}=\frac{8}{40}[/tex]So, it is expected to land 8 times on the red colour.
So answer is,
[tex]\frac{1}{5}=\frac{8}{40}[/tex]and It would be expected to land on red 8 times.
find the size of each interior angle of a regular hexagon
Answer:
Each interior angle = 180° -60° = 120°
Step-by-step explanation: We know that the three angles in a triangle, add up to 180°, and all the three angles are 60° in an equilateral triangle. The total number of angles of an enclosed space is 180° (n-2) where in is the number of sides.
A hexagon has six sides, so: s= 180° (6-2)
s= 180° x 4
s= 720°
now since in a regular shape, each interior angle is equal. We just divide the total interior angle with a number of sides
6.
720° divided by 6 is equal to 120°
A bag contains 3 gold marbles, 10 silver marbles, and 23 black marbles. You randomly select one marblefrom the bag. What is the probability that you select a gold marble? Write your answer as a reduced fractionPlgold marble)
ANSWER
P(gold marble) = 1/12
EXPLANATION
In total, there are:
[tex]3+10+23=36[/tex]36 marbles in the bag, where only 3 are gold marbles.
The probability is:
[tex]P(\text{event)}=\frac{\#\text{times the event can happen}}{\#\text{posible outcomes}}[/tex]In this case, the number of posible outcomes is 36, because there are 36 marbles in the bag. The number of times the event can happen is 3, because there are 3 gold marbles:
[tex]P(\text{gold marble)}=\frac{3}{36}=\frac{1}{12}[/tex]Find the parabola with focus (2,7) and directrix y = -1.
A parabola with focus (a, b ) and directrix y = c has the equation
[tex](x-a)^2+b^2-c^2=2(b-c)y[/tex]In our case, (a, b) = (2, 7) and c = -1; therefore, the above becomes
[tex](x-2)^2+7^2-(-1)^2=2(7-(-1))y[/tex][tex](x-2)^2+48=16y[/tex][tex]\Rightarrow\textcolor{#FF7968}{(x-2)^2=16(y-3)}[/tex]which is our answer!
