Given
There are 5 blue marbles, 2 red marbles, and 3 green marbles in a bag
[tex]\begin{gathered} \text{Total Marbles =5+2+3} \\ \text{Total Marbles =10} \end{gathered}[/tex]Probability of selecting a red marble
[tex]\text{Probability of selecting a red marble =}\frac{2}{10}=\frac{1}{5}[/tex]The final answer
The probability of selecting a red marble
[tex]\frac{1}{5}[/tex]Lines from Two Points (Point Slope Form) Write the equation of the line that passes through the points (0,8) and (−1,−4). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
1) The first thing to do is to find out the slope of the line that passes through points (0,8) and (-1,-4). We can do this using the Slope Formula:
[tex]m=\frac{-4-8}{-1-0}=\frac{-12}{-1}=12[/tex]2) Now, we need to find out the linear coefficient "b". Let's pick a point and plug it into the Slope-Intercept Formula with the slope:
[tex]\begin{gathered} y=mx+b \\ 8=12(0)+b \\ b=8 \end{gathered}[/tex]3) Then the answer is:
[tex]y=12x+8[/tex]what is the center and radius for the circle with equation (x-2)^2 + (y-5)^2=49
Solution
For this case we have the following equation given by:
[tex](x-2)^2+(y-5)^2=49[/tex]The general equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]And for this case by direct comparison we have:
[tex]r^2=49[/tex]Then we have:
[tex]r=\sqrt[]{49}=7[/tex]And the center si given by C=(h,k)
From the equation given we have:
[tex]C=(2,5)[/tex]what is .8 divided by 40
Problem
0.8 divided 40
Solution
We can do the following:
[tex]\frac{0.8}{40}=\frac{0.8\cdot10}{40\cdot10}=\frac{8}{400}[/tex]and if we simplify we got:
[tex]\frac{8}{400}=\frac{4}{200}=\frac{2}{100}=\frac{1}{50}=0.02[/tex]evaluate [tex]3 {x}^{2} - 4[/tex]when x=2.
3x^2 - 4 , at 2 is = 3•2^2 - 4
. = 12 - 4 = 8
If x decreases by 3 units what is the corresponding change in y ?
We have the equation:
[tex]y=6x-2[/tex]The rate of change in linear functions like this is equal to the slope, which in this case is m = 6.
So, for each unit increase in x, y will increase in 6 units.
[tex]\Delta y=m\cdot\Delta x=6\cdot1=6[/tex]This rate of change is constant for linear functions, so when x decreases by 3 units, we expect y to decrease by 3*6 = 18 units, 3 times the slope. So y will be -18 of the previous value.
[tex]undefined[/tex]Answer: a) 6, b) -18.
In the triangle below, if < C = 62 °, what is the measure of angle B?
In the given triangle ABC
[tex]BA=BC[/tex]Then the triangle is isosceles
In the isosceles triangle, the base angles are equal
Since [tex]m\angle A=m\angle C[/tex]Since m[tex]m\angle A=62^{\circ}[/tex]In any triangle the sum of angles is 180 degrees, then
[tex]m\angle A+m\angle B+m\angle C=180^{\circ}[/tex]Substitute angles A and C by 62
[tex]\begin{gathered} 62+m\angle B+62=180 \\ \\ m\angle B+124=180 \end{gathered}[/tex]Subtract 124 from both sides
[tex]\begin{gathered} m\angle B+124-124=180-124 \\ \\ m\angle B=56^{\circ} \end{gathered}[/tex]The answer is b
Law of Exponents. Simplify each expression. Answers should be written with positive exponents.(-5p^6 times r^-9)^0
Solution:
Given the expression:
[tex](-5p^6\cdot r^{-9})^0[/tex]Simplifying using the law of exponents,
[tex]\begin{gathered} (-5p^6\cdot r^{-9})^0=(-5\times p^{-6}\times r^{-9})^0 \\ \end{gathered}[/tex]but
[tex]a^{-b}=\frac{1}{a^b}[/tex]thus, we have
[tex]\begin{gathered} (-5\times p^{-6}\times r^{-9})^0=(-5\times\frac{1}{p^6}\times\frac{1}{r^9})^0 \\ =(-\frac{5}{p^6r^9})^0 \end{gathered}[/tex]From the zero index law of exponents,
[tex]a^0=1[/tex]This implies that
[tex](-\frac{5}{p^6r^9})^0=1[/tex]Hence, the solution to the expression is 1
Solve the system of two linear inequalities graphically.{x<5<2x - 4Step 1 of 3: Graph the solution set of the first linear inequality.Answer3 KeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.HOANChoose the type of boundary line:O Solid (-)Dashed ---)SEnter two points on the boundary line:10-5ज510JOO5Select the region you wish to be shaded:ОАOB101
From the problem, we have :
[tex]\begin{gathered} x<5 \\ x\ge-4 \end{gathered}[/tex]For the first inequality, x < 5
Since the symbol is "<", the boundary line is dashed line.
The boundary line is at x = 5 which has points (5, 0) and (5, 2)
and the region is to left of x = 5.
The graph will be :
Next is to graph the second inequality, x ≥ -4
Since the symbol is "≥", the boundary line is a solid line
The boundary line is at x = 4 which has points (-4, 0) and (-4, 2)
and the region is to the right.
The graph will be :
The solution to the inequalities is the overlapping region when joined together.
This will be :
The overlapping region is the middle region or region in between the boundary line which is also -4 ≤ x < 5
The table shows how the number of sit-ups Marla does each day has changed over time. At this rate, how many sit-ups will she do on Day 12? Explain your steps in solving this problem.see image
Maria willdo 61 sit-ups on Day 12
Explanation
the table represents a linear function so, we can find the equation of the function and then evaluate for day 12
the equation of a line is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]so
Step 1
find the slope of the line
the slope of a line is given by.
[tex]\begin{gathered} \text{slope}=\frac{change\text{ in y }}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \\ \text{are 2 points from the table } \\ or\text{ 2 coordinates ( from the table)} \end{gathered}[/tex]let
P1(1,17)
P2(4,29)
now, replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{29-17}{4-1}=\frac{12}{3}=4 \\ \text{slope= 4} \end{gathered}[/tex]Step 2
now,find the equation of the line,use the slope-point formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope} \\ \end{gathered}[/tex]now, replace
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-17=4(x-1) \\ y-17=4x-4 \\ y=4x-4+17 \\ y=4x+13 \end{gathered}[/tex]so,the equation of the lines is
y= 4x+13
Step 3
finally, evaluate for day 12, it is x= 12
so,replace
[tex]\begin{gathered} y=4x+13 \\ y=4(12)+13 \\ y=48+13 \\ y=61 \end{gathered}[/tex]it means Maria will do 61 sit-ups on Day 12
I hope this helps you
If 2/3rd of a trail is 3/4ths of a mile, how long is the whole trail?
Answer:
1 1/2 or 1.5 miles
Step-by-step explanation:
we can multiply 3/4 by 2/3 to see how many miles is in each third of a trail
3/4*2/3=6/12
1/2 of a mile per third of the trail so now we multiply by 3 to get whole trail
1/2 x/3/1=3/2
3/2= 1 1/2
Hopes this helps please mark brainliest
Rewrite the equation below so that it does not have fractions. 3+ = x= = Do not use decimals in your answer.
First we have to find the least common multiple between the denominators ( 3 and 7). Since they are prime numbers the LCM is : 3*7 = 21
Then, multiply each term of the equation by 21 and simplify
[tex]\begin{gathered} 3\cdot21+21\cdot\frac{2}{3}x=\frac{2}{7}\cdot21 \\ 63+7\cdot2x=2\cdot3 \\ 63+14x=6 \end{gathered}[/tex]The answer is 63 + 14x = 6
23 The list gives information about the favorite color of each of 22 students.• 6 students chose red.• 2 students chose yellow.• 5 more students chose blue than yellow.• 3 fewer students chose purple than red.• The rest of the students chose green.Which frequency table represents the number of students who chose each color?
ANSWER
Option B
EXPLANATION
We are given the information regarding favorite colors of 22 students.
=> 6 students chose red.
=> 2 students chose yellow.
=> 5 more students chose blue than yellow.
Let the number of students that chose blue be b. This means that:
b = yellow + 5
b = 2 + 5
b = 7 students
7 students chose blue.
=> 3 fewer students chose purple than red.
Let the number of people that chose purple be p. This means that:
p = red - 3
p = 6 - 3
p = 3 students
3 students chose purple.
=> The rest of students chose green.
To find the number of students that chose green, add up the number of students that chose the other colors and subtract from the total number of students.
That is:
22 - (6 + 2 + 7 + 3)
22 - 18
= 4 students
4 students chose green.
Therefore, the correct frequencey table is option B.
1. Find the value of x.
2. Find the value of t.
Answer:
x=15
t=2
Step-by-step explanation:
to find x both of these triangles have the same angle measure and we know 2 of them and the sum of all three angles of a triangle always equal 180 degrees
45+90=135
Now we subtract from 180
180-135=45
45 degrees is what 3x is equal to so to figure out X just set 3x equal to 45
3x=45
/3. /3
x=15
Now to find t the 2 sides in the bottom of the triangle are equivalent so we can set them equal to each other
2t=4
/2. /2
t=2
Hopes this helps please mark brainliest
x + y + zX=5 y=3 z=7
Describe how the graph of y = ln (-x) relates to the graph of its parent function y = ln x.
The graph of function f(-x) can be obtained from graph of pareant funcion f(x) by refecting the graph over y-axis.
We need to obtain the graph of ln (-x) from parent function ln x, which is nothing but replace of x by -x. So graph of ln (-x) is obtained by reflection of graph of function ln (x) over y-axis.
Answer: y-axis reflection
Calculate the limitlim x => -4 [tex] \frac{x {}^{2} + 2x - 8}{x {}^{2} + 5x + 4} [/tex]
The limit to be calculated is:
[tex]\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}[/tex]Notice that:
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+5x+4}=\frac{(x-2)(x+4)}{(x+1)(x+4)} \\ =\frac{(x-2)}{(x+1)},x\ne-4 \end{gathered}[/tex]Remember that, in the limit when x->-4, the value of x approaches to -4, but it never is -4. Thus, we can use the last line of the identity above,
[tex]\begin{gathered} \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=\lim _{x\to-4}\frac{(x-2)(x+4)}{(x+1)(x+4)}=\lim _{x\to-4}\frac{(x-2)}{(x+1)}=\frac{(-4-2)}{(-4+1)}=-\frac{6}{-3}=2 \\ \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=2 \end{gathered}[/tex]The answer is 2.
The volume of a large tank is 350 ft. It is 65 ft wide and 4 ft high. What is the length of the tank?
The volume of a rectangular prism can be calculated by the formula
[tex]V=l\cdot w\cdot h[/tex]in which l, w and h represent the length, width, and heght respectively.
clear the equation for l
[tex]l=\frac{V}{w\cdot h}[/tex]replace with the data given
[tex]undefined[/tex]Martha drove her car east for a total of 9 hours at a constant velocity. In one-third of that time, she drove 180 kilometers. What was her velocity?
time = one third of 9 hours = 1/3 x 9 = 3 hours
Distance = 180 km
Velocity = Distance / time
Replacing:
V = 180 km/3 h = 60 km per h
Find the sales tax.
Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$70.00
3%
?
The sales tax is $.
Answer: $2.10
Step-by-step explanation: 3% of $70 is $2.10.
The total cost would be $72.10
How to calculate percentages:
Divide the number that you want to turn into a percentage by the whole. In this example, you would divide 2 by 5. 2 divided by 5 = 0.4. You would then multiply 0.4 by 100 to get 40, or 40%.
The Voronoi diagram below shows the locations of the four post offices P_{1} , P_{2} P_{3} , and P_{4}in a city.y(km)8P_{3}P2r (km)6P_{1}PKatie's apartment lies inside the shaded circle shown on the diagram.(a) Write down the post office nearest to Katie's apartment.P is located at coordinates (3-6), and the edge between P and P_{i} has the equation y = - 5/3 * x = 16/3(b) Determine the location of PPa is located at coordinates (1.7).3(c) Find the gradient. A. of the edge between P, and P.
Given -
Voronoi diagram:
To Find -
(a) Write down the post office nearest to Katie's apartment.
(b) Determine the location of P4
(c) Find the gradient k. of the edge between P3 and P4
Step-by-Step Explanation -
(a)
We can see from the voronoi diagram that the center of the x-axis where the circle covers is where Katie's apartment is located.
It is located near P4.
So,
P4 is nearest to Katie's apartment.
(b)
The location of P4:
(2, -3)
(c)
[tex]k\text{ = }\frac{Y_2\text{ - Y}_1}{X_2\text{ - X}_1}\text{ = }\frac{7}{50}[/tex]Final Answer -
(a) The post office nearest to Katie's apartment = P4
(b) The location of P4 = (2, -3)
(c) The gradient k of the edge between P3 and P4 = 7/50
in the figure shown Sigma MN is parallel to y z what is the length of segment MX
We will solve for MX using similar angles theorem
Let line MX be= y
we have to find the ratio of the small triangle to that of the big triangle
Therefore we will have,
[tex]\begin{gathered} \frac{\text{xcm}}{(x+12)cm}=\frac{3.5\operatorname{cm}}{17.5\operatorname{cm}} \\ \text{when we cross multiply we wil have,} \\ 17.5\times x=3.5(x+12) \\ 17.5x=3.5x+42 \\ by\text{ collecting like terms we wll have} \\ 17.5x-3.5x=42 \\ 14x=42 \end{gathered}[/tex]to get x we divide both sides by the coefficient of x which is 14
[tex]\begin{gathered} \frac{14x}{14}=\frac{42}{14} \\ x=3.0\operatorname{cm} \end{gathered}[/tex]Hence ,
[tex]\vec{MX}=3.0\operatorname{cm}[/tex]Therefore,
The correct option will be OPTION A
Q4 O center (-1,3), radius = 1 What is the center and radius of the circle, 2 2 r + y + 2x - 6y +9=0 - 9 center (1,-3), radius = 1 center (-1,3), radius = 9 center (1,-3), radius = 3
Step 1: Write out the formula
The equation of a circle given by
[tex](x-a)^2+(y-b)^2=r^2[/tex][tex]\begin{gathered} \text{where} \\ (a,b)\text{ is the center of the circle} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given equation and rewrite it in the form shown above
[tex]x^2+y^2+2x-6y+9=0[/tex][tex]\begin{gathered} x^2+2x+y^2-6y+9=0 \\ \text{ By completing the square, we have} \\ (x+1)^2-(+1)^2+(y-3)^2-(-3)^2+9=0 \\ \end{gathered}[/tex][tex]\begin{gathered} (x+1)^2+(y-3)^2-1-9+9=0 \\ (x+1)^2+(y-3)^2=1=1^2 \end{gathered}[/tex]By comparing the equation with the formula above, we have
[tex]a=-1,b=3,r=1[/tex]Therefore,
center (-1,3), radius = 1
By the Remainder Theorem, what can be said about the polynomial function w(x) if w(−5)=3 ?
the remainder must be _________ when w(x) is divided by _________
thanks so much!
well, ding ding ding!! let's recall the remainder's theorem
if some function f(x) has a factor of say x - a, then if we plug the "a" in f(x) what we get is the remainder, that is, the remainder in a division of f(x) by (x-a).
all that mouthful said, well, since we know of w(-5), that means w(x) must have a factor of x - (-5) or namely x + 5.
we also know that w(-5) = 3, well, that means that 3 is the remainder of such division, that is, w(x) ÷ (x + 5), gives us a remainder of 3.
Given the definitions of f(x) and g(2) below, find the value of g(f(-3))f(x) = -3x – 12g(x) = 3x2 – 2x – 14
Given data:
Itis given that
[tex]\begin{gathered} f(x)=-3x-12 \\ g(x)=3x^2-2x-14 \end{gathered}[/tex]Now to calcualte g(f(-3)) first let us calculate f(-3)
[tex]\begin{gathered} f(-3)=-3(-3)-12 \\ =9-12 \\ =-3 \end{gathered}[/tex]Now, g(f(-3)) will be
[tex]\begin{gathered} g(f(-3))=g(-3) \\ =3(-3)^2-2(-3)-14 \\ =3(9)+6-14 \\ =27-8 \\ =19 \end{gathered}[/tex]So, value of g(f(-3)) is 19.
Solve fir X in the equation?
First, find the missing angle of the triangle. Remember that the internal angles of a triangle should add up to 180°, then, the missing angle is given by:
[tex]180-64-27=89[/tex]On the other hand, the angle of 89° plus the angle of (97+x)° should add up to 180 since they are adjacent angles on a straight line. Then:
[tex]89+(97+x)=180[/tex]Solve for x:
[tex]\begin{gathered} \Rightarrow89+97+x=180 \\ \Rightarrow186+x=180 \\ \Rightarrow x=180-186 \\ \Rightarrow x=-6 \end{gathered}[/tex]Therefore, the value of x is:
[tex]-6[/tex]is 0.343434343434 rational or irrational, explain how u know
EXPLANATION
The number 0.343434343434 is a periodic number rational because the all the periodic numbers are rational ones.
chance the pilot of a boeing 727 flew e plane so it took off at an angle of elevation 21 degrees. after flying one kilometer, what is the altitude (height) of the plane that chance was flying rounded to the nearest meter? (1 km= 1000 meters)
To solve the exercise, it is convenient to first draw a picture of the situation posed by the statement:
As you can see, a right triangle is formed. So to find the height at which the plane was when the pilot had flown one kilometer, you can use the trigonometric ratio sin(θ):
[tex]\sin (\theta)=\frac{\text{Opposite side}}{\text{ Hypotenuse}}[/tex]Then, in this case, you have
[tex]\begin{gathered} \sin (21\text{\degree})=\frac{\text{ Altitude}}{1000m} \\ \text{ Multiply by 1000m on both sides of the equation} \\ \sin (21\text{\degree})\cdot1000m=\frac{\text{ Altitude}}{1000m}\cdot1000m \\ \sin (21\text{\degree})\cdot1000m=\text{ Altitude} \\ 358.37m=\text{ Altitude} \\ \text{ Rounding to the nearest meter} \\ 358m=\text{ Altitude} \end{gathered}[/tex]Therefore, the altitude or height of the plane after flying one kilometer is 358 meters.
can you please help me
Answer
The graph of y = -3x + 1 is presented below
Explanation
We are asked to plot the graph of y = -3x + 1
We will use intercepts to obtain two points on the line and connect those two points
y = -3x + 1
when x = 0
y = -3x + 1
y = -3(0) + 1
y = 0 + 1
y = 1
First point on the line is (0, 1)
when y = 0
y = -3x + 1
0 = -3x + 1
3x = 1
Divide both sides by 3
(3x/3) = (1/3)
x = ⅓ = 0.333
Second point on the line is (⅓, 0) or (0.333, 0)
The graph of this question is presented under 'Answer' above.
Hope this Helps!!!
Hello!I have (m^3n^5)^1/4 and I do not know how to take the n out since it is n^5/4.Thanks
We are given
[tex](m^3n^5)^{\frac{1}{4}}[/tex]
We want to take n out
Solution
Given
[tex]\begin{gathered} (m^3n^5)^{\frac{1}{4}} \\ (m^3\times n^4\times n)^{\frac{1}{4}} \\ (m^3)^{\frac{1}{4}}\times(n^4)^{\frac{1}{4}}\times(n)^{\frac{1}{4}} \\ (m^3)^{\frac{1}{4}}\times n^{}\times(n)^{\frac{1}{4}} \\ n\times(m^3)^{\frac{1}{4}}^{}\times(n)^{\frac{1}{4}} \\ n(m^3n)^{\frac{1}{4}} \end{gathered}[/tex]Determine which of the following statements is NOT correct
THe statement that is not correct is the first one