Multiplication:
Lisa, Bret, and Gary harvested apples. If they each harvested 3 carts of apples, how many carts did they harvest in total?
--> 3 * 3 = 9 carts in total
Division:
Lisa, Bret, and Gary harvested apples. If all three of them harvested 9 carts of apples in total, how many carts did each person harvest.
--> 9 / 3 = 3 carts per person
How to make 9/2=x/24 a equation
Answer:
I wasn't too sure of your question, but this is what made sense to me.
Step-by-step explanation:
cross multiplication seems to be the best fit for this.
Like this:
[tex]\frac{9}{2}=\frac{x}{24}\\ 2(x)=9(24)\\ 2x=216\\x= \frac{216}{2}\\ x=108[/tex]
Hope this helped in any way.
Find anequation for the perpendicular bisector of the line segment whose endpoints are(-8, 4) and (-4,-8).
to solve this question, we need to difine our variables
we have values for end points as
x1 = -8
y1 = 4
x2 = -4
y2 = -8
next we can find the slope of the equation
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-8-4}{-4-(-8)} \\ \text{slope}=\frac{-12}{4} \\ \text{slope}=-3 \end{gathered}[/tex]step 2
let's find the mid-point using mid-point formula
[tex]\begin{gathered} md=\frac{x_1+x_2}{2},\frac{y_2+y_1}{2} \\ md=\frac{-8+(-4)}{2},\frac{-8+4}{2} \\ md=-6,-2 \end{gathered}[/tex]mid-point = (-6, -2)
now we know the perpendicular line travels (-6 , -2) and has a slope of -3
equation of a straight line => y = mx + c
we can solve for c to find the equation.
[tex]\begin{gathered} y=mx+c \\ -2=(-3)(-6)+c \\ -2=18+c \\ c=-2-18 \\ c=-20 \end{gathered}[/tex]note: m = slope
c = intercept
the equation of the perpendicular bisector can be written as
y = -3x - 20
[tex]y=-3x-20[/tex]MATH HELP PLEASEEEE 35 POINTS
Answer:
Step-by-step explanation:
3.75 is a2 x (b-c)
4.85 gose with the b + c -a
3.3 gose to the a - b + c
you should now know the last one
Answer:
1. A² × ( B - C ) = 3.75
2. B + C - A = 3.65
3. A - B + C = 4.85
4. B × ( A - C ) = 3.3
Step-by-step explanation:
1. (5 × 5) × (4.4 - 4.25)
25 × .15 = 3.75
2. (4.4 + 4.25) - 5
8.65 - 5 = 3.65
3. (5 - 4.4) + 4.25
.6 + 4.25 = 4.85
4. 4.4 × ( 5 - 4.25 )
4.4 × .75 = 3.3
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Convert 21,510 ft to mi
Answer:
4.0738636
Step-by-step explanation:
Estimate sqrt(37) to the nearest tenth. Then locate sqrt(37) on a number line.137 =(Round to the nearest tenth as needed.)
The given number is
[tex]\sqrt{37}[/tex]Which is equal to 6,0827625302982196889996842452021...
However, rounded to the nearest tenth is
[tex]\sqrt{37}\approx6.1[/tex]The image below shows the number graphed on a number line.
write 1.09 × 10^-4 in standard notation
1.09 × 10^-4 in standard form is
[tex]\text{ 1.09 x 10}^{-4}[/tex]What is the answer to this?
Answer: 4/7
Step-by-step explanation:
There are 7 students with brothers, 4 of which have sisters.
So, the probability is 4/7.
the wholesale price for a pair of shoes is $5.50. A certain department store marks up the wholesale price by 40%. Find the price of shoes in the department store.
EXPLANATION
Price of shoes = $5.50
Markup= 40%
Let's call x to the unknown final price.
The markup percentage relationship is given by the following formula:
[tex]\text{Markup =( }\frac{Selling\text{ Price}-\text{Cost Price}}{\text{Cost Price}})\cdot100[/tex]Replacing terms:
[tex]\text{40}=(\frac{x-5.5}{5.5})\cdot100[/tex]Multiplying both sides by 5.5:
[tex]40\cdot5.5=(x-5.5)\cdot100[/tex]Dividing both sides by 100:
[tex]\frac{40\cdot5.5}{100}=x-5.5[/tex]Adding 5.5 to both sides:
[tex](\frac{40\cdot5.5}{100})+5.5=x[/tex]Simplifyng the fraction:
[tex]2.2+5.5=x[/tex]Adding numbers:
[tex]\text{7}.7\text{ = x}[/tex]Switching sides:
[tex]x=7.7[/tex]Answer: The final price of the shoes in the deparment store is $7.7
Part A and B answer snd explaintion please
Answer:
Step-by-step explanation:
63 and 117
I need help with this worksheet that’s due tomorrow for algebra 1 it’s about Characteristics of Quadratic Functions
We have the following quadratic Function in a graph:
Now, we solve one aspect at a time:
Zeros
Let's remember that the zeros or roots of the quadratic function are those values of x for which the expression is 0. Graphically, the roots correspond to the abscissae of the points where the parabola intersects the x-axis.
By looking at the graph we can identify these, which in this case it is:
[tex](-2,0)[/tex]Axis of symmetry
Recall that the graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola.
By looking at the graph we can identify this, which in this case it is:
[tex]x=-2[/tex]Max or min
In mathematical analysis, the maxima and minima of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range or on the entire domain.
By looking at the graph we can identify this, which in this case it is:
[tex]y=0[/tex]Vertex
Remember that the vertex of a quadratic equation or parabola is the highest or lowest point of the graph corresponding to that function. The vertex lies in the plane of symmetry of the parabola; whatever happens to the left of this point will be an exact reflection of what happens to the right.
By looking at the graph we can identify this, which in this case it is:
[tex](-2,0)[/tex]Margaret can fit 17 pencils in a small box and 50 pencils in a large box. She has 10 small boxes of pencils and would like to reorganize the pencils into large boxes. How many large boxes could she fill?
Answer:
She can fill five boxes with 20 pencils left over.
Step-by-step explanation:
17x10=170
170/50=3.4
50x3=150
170-150=20
In triangle ABC, the segments drawn from the vertices intersect at point G. Segment FG measures 6 cm, and segment FC measures 18 cm. Which best explains whether point G can be the centroid? (are the answers given here right? cos I'm not quite sure)
A centroid divides each median in a ratio 2:1, in this case, the segment FC is the sum of the segments FG and GC:
[tex]FC=FG+GC[/tex]By solving for GC, we get:
[tex]GC=FC-FG=18-6=12[/tex]Then, the part of the median that goes from C to G has a length of 12 and the part that goes from the centroid to F has a length of 6, then we can express their ratio as 12:6, which is equivalent to 2:1.
Then the answer is:
Point G can be the centroid because 12:6 equals 2:1
NO LINKS!! Please help me with this probability question
===========================================================
Explanation:
Define these two events
A = father born in Michigan
B = mother born in Michigan
The notation ~A and ~B represent the opposite of each defined event above.
According to the table
P(A) = 0.48
P(B) = 0.73
If A and B were independent, then P(A and B) = P(A)*P(B) = 0.48*0.73 = 0.3504 = 35.04% but this contradicts the 29% in the "father born in Michigan" column and "mother born in Michigan" row. The table states that P(A and B) = 0.29 should be the case instead of 0.3504.
Because of this contradiction, this means P(A and B) = P(A)*P(B) is false and therefore A and B are NOT independent
--------------------------------------
Another way to look at it:
P(A) = 0.48
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.29/0.73
P(A given B) = 0.39726 approximately
If A and B were independent, then P(A) and P(A given B) would be the same value. However, they are not. This is another way to see why the events are NOT independent
Through similar calculations, P(B given A) = P(A and B)/P(A) = 0.29/0.48 = 0.6042 approximately which doesn't match with P(B) = 0.73; if A and B were independent then P(B) needs to be equal to P(B given A).
HELP ME ASAPPP
Mr. Anderson worked with the following number of students each year.
42 in 2023-2024
256 in 2022-2023
195 in 2021-2022
228 in 2020-2021
174 in 2019-2020
136 in 2018-2019
216 in 2017-2018
204 in 2016-2017
151 in 2015-2016
What would we call 42 in this situation?
A.
Mean Absolute Deviation
B.
Mode
C.
Outlier
D.
Range
What is the solution and working?
The value of the length AB xcm = -3½ which is derived using the completing the square method, and satisfies the expression 2x² - 5x - 42 = 0.
Completing the square methodTo solve for the unknown value of a quadratic equation; say ax² + bx + c = 0:
First make the coefficient of x² one by dividing through by "a"Move the constant "c" to the right hand side of the equationDivide the coefficient of "x" by 2, square the result and add to both sides of the equation.The left hand side of the equation would have a complete square which will then be easier to solve for the value "x".From the derived quadratic equation, applying the method of completing the square as follows;
2x² - 5x - 42 = 0
divide through by 2
x² - (5/2)x - 21 = 0
add 21 to both sides
x² - (5/2)x = 21
divide the coefficient of x, square the result and add it to both sides
x² - (5/2)x + (5/4)(5/4) = 21 + (5/4)(5/4)
factor the left hand side of the equation
(x - 5/4)² = 21 + (25/16)
simplify the right hand side
(x - 5/4)² = 361/16
take the square root of both sides
x - 5/4 = (+ or -)(19/4)
then;
x = 5/4 + 19/4 or 5/4 - 19/4
x = 3 or x = -3½
The quadratic equation 2x² - 5x - 42 = 0 is true for the value of x = -3½.
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The graph shows a coordinate plane that goes from negative 8 to 8 in each direction. The graph also shows two lines that intersect at ( 2 , 3 ). That point is labeled "solution." That's right. When you have two or more linear equations, it is called a "system of linear equations". The solution to a system of linear equations consists of the - and -value that make BOTH equations true. Graphically, this appears as the point where the lines intersect. In this case, the solution is the ordered pair , as shown on the graph. If you are trying to decide whether a system of equations has a solution, would you rather have the equations or the graphs? Why?
To visualize the solution of a system of equations, a graph is ideal, as we can see whether the functions intersect or not.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem. The pair/tuple/... containing these values is called the solution of the system.
The equations that construct a system are functions, and the solution of a system is at the point of intersection of these functions. The intersection of two points is easier to visualize graphically then calculating, hence a graph is ideal, as we can see whether the functions intersect or not, while for the function we would have to calculate.
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give the answer, which of the following are composite numbers? 4 9 15 3 5
Given
we are given numbers 4, 9, 15, 3, 5
Required
we need to find which of the above numbers are composite.
Explanation
Here
[tex]\begin{gathered} 4=2\times2 \\ 9=3\times3 \\ 15=3\times5 \\ 3=3\times1 \\ 5=5\times1 \end{gathered}[/tex]clearly 4, 9, 15 have factors other than 1 and itself.
so 4, 9 and 15 are composite numbers
3х2 + 14х — 49 = 0solve for x
The given expression 3x^2 +14x-49=0
we will de factorization tos solve for x
[tex]\begin{gathered} 3x^2+14x-49=0 \\ 3x^2-7x+21x-49=0 \\ (3x^2-7x)+(21x-49)=0 \\ \text{Taking x common from (}3x^2-7x)=x(3x-7) \\ \text{Taking 7 common from }(21x-49)=7(3x-7) \\ (3x^2-7x)+(21x-49)=0 \\ x(3x-7)+7(3x-7)=0 \\ \text{Taking (3x-7) common} \\ (3x-7)(x+7)=0 \\ \text{ Thus, for} \\ \text{(3x-7)=0} \\ 3x=7 \\ x=\frac{7}{3} \\ \text{and for (x+7)=0} \\ x+7=0 \\ x=-7 \end{gathered}[/tex]The value of x is -7 and 7/3
Answer : x = -7 and x = 7/3
The earth's average distance from the sun is 92,960,000 miles. Venus’s distance from the sun is an average of 67,230,000 miles. The Earth is how much farther from the sun than Venus? Express the answer in scientific notation.
Answer:
[tex]2.573 \times 10^7[/tex]
Step-by-step explanation:
[tex]92960000-67230000=25730000=2.573 \times 10^7[/tex]
please help me ASAP!!
We have to solve:
[tex]\begin{gathered} 2^x-3=(x-6)^2-4_{} \\ 2^x-3+4=(x-6)^2 \\ 2^x+1=(x-6)^2 \end{gathered}[/tex]We can not write a explicit expression to find the value of x, but we can test each option to see which one is correct:
[tex]\begin{gathered} x=5 \\ 2^5+1=(5-6)^2 \\ 33=(-1)^2\longrightarrow\text{Not true} \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ 2^3+1=(3-6)^2 \\ 8+1=(-3)^2 \\ 9=9\longrightarrow\text{True} \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ 2^4+1=(4-6)^2 \\ 17=(-2)^2\longrightarrow\text{Not true} \end{gathered}[/tex][tex]\begin{gathered} x=-2 \\ 2^{-2}+1=(-2-6)^2 \\ \frac{1}{4}+1=(-8)^2\longrightarrow\text{Not true} \end{gathered}[/tex]Answer: x=3
Sketch a graph of 6 x + 4 y = 4
The graph of 6x + 4y = 4 can be sketched as shown in the image attached below.
How to Sketch the Graph of a Linear Equation?A linear equation can be expressed in standard form as Ax + By = C, where A, B, and C are integers. Also, it can be rewritten in slope-intercept form as y = mx + b, where b is the y-intercept and m is the slope of the equation.
In order to graph an equation, we can easily determine what the slope (m) and the y-intercept (m) of the graph would be when we rewrite the equation in slope-intercept form.
Given the equation in standard form as, 6x + 4y = 4, rewrite it in slope-intercept form:
6x + 4y = 4
4y = -6x + 4
y = -6x/4 + 4/4
y = -3/2x + 1
This means that the slope of the graph you'd sketch will be -3/2, and the line must intercept the y-axis at 1, because the y-intercept is 1.
The graph is shown below.
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Please help with this math problems! This is due in a few hours!
(i) The vertex's x-coordinate is 25.
(ii) The maximum height of the cannonball is 12.48 meters.
(iii) Total horizontal distance that a cannon ball can travel is 50 meters.
(iv) Total horizontal distance that a cannon ball can travel with decreased angle is 22.5 meters.
(v) Distance the cannonball traveled before reaching the maximum height is 25 meters.
What is coordinate?
A pair of values is used to specify a point's placement on a coordinate plane using both horizontal and vertical distinctions from the two separate axes. usually represented by a pair of x-values and y-values (x,y).
(i) They are both at y = 4 and separated by (40-10) = 30
The symmetry line is halfway between 40 and 10
Consequently, the vertex's x-coordinate is 25.
(ii) y = -0.01x2 + 0.5x,
a = -0.01,
b = 0.5,
-b/2(a) = -0.5/(2X-0.01) = 0.5/0.02, and so on.
y=-0.01*2+0.5(25) =12.48 meters
The maximum height of the cannonball is 12.48 meters.
(iii) Total horizontal distance that cannon ball can travel is (0,0)-(50,0)= 50 meters.
(iv)Total horizontal distance that cannon ball can travel with decreased angle is (0,0)-(22.5,0) =22.5 metres
(v) Distance cannon ball travelled before reaching the maximum height is [(0,0)-(50,0)]/2 =25 meters
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Human hair grows at a rate of about 6.849×10-4 cm per hour to 2.329×10−2 cm per hour. The rate depends on gender, genetics, age, and health. Find the difference between the high end and the low end of the range. Express your answer in scientific notation rounding to 2 decimal places.
Answer:
2.×10^-2 cm/h . . . . rounded to 2 dp
2.26×10^-2 cm/h . . . . rounded to 3 sf
Step-by-step explanation:
You want the difference in growth rates between 6.849×10^-4 cm per hour and 2.329×10^-2 cm per hour.
DifferenceThe difference of two numbers written in scientific notation requires that they have the same power-of-ten multiplier.
2.329×10^-2 - 6.849×10^-4
= 2.329×10^-2 - 0.06849×10^-2 = 2.26051×10^-2 = 0.0226051
RoundingThe question asks for the answer rounded to 2 decimal places and expressed in scientific notation.
0.0226051 ≈ 0.02 = 2×10^-2 . . . . cm per hour
It makes more sense to round the mantissa to 2 decimal places, meaning the value is rounded to 3 significant figures.
2.26051×10^-2 ≈ 2.26×10^-2 . . . . cm per hour
find perimeter and area of each triangle round to nearest hundredth
Given is a right angled triangle. Consider the figure,
Using the trignoetric funcyion tan, we have,
[tex]\begin{gathered} \tan 18=\frac{a}{12} \\ a=12\times\tan 18=3.89 \end{gathered}[/tex]Now, as we have base, a = 3.89 and height c = 12, the perimeter can be calcualted as,
[tex]\begin{gathered} P=a+c+\sqrt[]{a^2+c^2} \\ \text{ =3.89+12+}\sqrt[]{3.89^2+12^2}=28.5=29 \end{gathered}[/tex]Now, the area can be calculated as,
[tex]\begin{gathered} A=\frac{1}{2}ac \\ \text{ =1/2}\times3.89\times12=23.34=23 \end{gathered}[/tex]can you please list 1-6 if they are rational irrational integer whole and natural
1. -14/2 = -7 Integer, Rational
2. √64 = 8 Natural, Whole, Integer, Rational
3. 0 Whole, Integer, Rational
4. π Irrational
5.
[tex]0.\bar{45}[/tex]can be expressed as a fraction, then it's rational
6. 3/8 Rational
22% of the squirrels in Cititon Park are gray. What is the probability that, in a random sample of 322
squirrels, fewer than 71 are gray squirrels? Use a normal approximation to compute your answer.
Round your answer to 4 decimal places.
The probability is 0.4841 .
Probability theory is the name of the branch of mathematics that deals with probability.
Although there are many ways to interpret the concept of probability, probability theory approaches it in a formal mathematical manner by articulating it through a set of axioms. These axioms typically formalize probability in terms of a probability space, which connects a sample space of possible outcomes to a measure that accepts values between 0 and 1. Statistical mechanics or sequential estimation are two examples of how probability theory approaches can be used to describe complicated systems when only a piece of their state is known. A significant achievement in twentieth-century physics was the description of the probabilistic nature of physical events at the atomic scale in terms of quantum mechanics.Given n = 322
p = 0.22
We know that from probability
μ = n × p = 0.22 ×322 = 70.84
σ = √(p × n×(1-p)) = 7.43
Now (P < 71) = P<70.84
Solving we get
P(z<-0.045)
= 0.48405
Therefore the probability is 0.4841
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The area of the desert is 25,000 square miles a scale drawing of the desert has a scale drawing 10 square inches. What is the scale of the map?
The scale of the map is 1 square inches = [tex]10^{13}[/tex] square inches.
Given that:-
Area of the desert = 25,000 square miles
Area of the desert in the map = 10 square inches
We have to find the scale of the map.
We know that,
1 mile = 63360 inches
Hence, conversion of square miles to square inches:-
1 mile * 1 mile = 63360 inches *63360 inches
1 square mile = 4,01,44,89,600 square inches
25,000 square miles = 40144893600*25000 = 10,03,62,24,00,00,000 square inches =[tex]10.036224 *10^{13}[/tex] ≈ [tex]10*10^{13}[/tex] square inches.
Now, we can say that [tex]10*10^{13}[/tex] square inches is scaled to 10 square inches.
Hence, the scale of the map is :-
1 square inches = [tex]10^{13}[/tex] square inches.
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Please see photo I think it is the first answer but I wanted to confirm
Hello
The sample which she has to study is 200
The answer to this question is option A
Thank for helping have a great rest of your night
The number of red balloons is 5.
The number of blue balloons is 7.
The number of yellow balloons is 12.
ExplanationTo find the probability of randomly selected a yellow balloon
[tex]P=\frac{number\text{ of red balloons}}{total\text{ number of balloons}}[/tex][tex]\begin{gathered} P=\frac{12}{5+7+12} \\ P=\frac{12}{24} \\ P=\frac{1}{2} \end{gathered}[/tex]AnswerHence the correct option is C that is 1/2.
What property is being used here?
4x-3
x=2
4(2)-3
THE PROPERTY OF SUBSTITUTION IS USED. IF x=2 IT MEANS IN THE PLACE OF X IN THE EXPRESSION 4X-3 YOU WILL PLUG IN THE VALUE 2 AND SIMPLIFY.
[tex] = 4(2) - 3 \\ = 8 - 3 \\ = 5[/tex]
JUST AS I HAVE DONE ABOVE.
HOPE THIS HELPS