The median weight is the value that divide the sample of wights into a higer half and a lower half.
To find the median wight, first we must put the weights in crescent order:
9, 9, 9, 10, 13, 14, 15
Then, we can check that 10 pounds is the median weight, since there is three lower weights on its left {9,9,9} and three higer weights on its right {13, 14, 15}
Finally, the mean is caculated by the sum of the weights of each cat divided by the total number of cats:
[tex]\frac{13+15+9+9+9+14+10}{7}=\frac{79}{7}\approx11.3\text{ pounds}[/tex](-3, 1) is translated 1 unit right
Given point ( -3, 1)
we need to translate it 1 unit right
So, the rule will be:
[tex](x,y)\rightarrow(x+1,y)[/tex]so, the point after translation will be:
[tex](-3,1)\rightarrow(-2,1)[/tex]So, the answer will be: ( -2, 1 )
Find the slope of the line passing through the points (-3, 3) and (5, 9).
Answer:
slope = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (5, 9 )
m = [tex]\frac{9-3}{5-(-3)}[/tex] = [tex]\frac{6}{5+3}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
Dawn simplified a power correctly and came up with a value of 64.Which could have been the original exponential form of the expression Dawn simplified? Check all that apply.A. (–4)3B. 26C. 34D. (–8)2E. (–2)6
We have to find the ones that simplified are equal to 64. Thos are (-8)^2 and (-2)^6. So the answer are D and E
Which image shows the correct position of M(-4, 3)?
A. graph A.
B. graph B.
C. graph C.
D. graph D.
Answer:
Graph A
Step-by-step explanation:
The x coordinate is -4 and the y coordinate is 3.
Figures I to VI represent one of the six situations described below. Match each graph to the situation it describes. 1 ) the temperature as the weather changes from rainy to snowy_________2) the number of fish caught per hour on a bad fishing day__________ 3) the total amount of rain that falls on a rainy day ____
1) The temperature when the weather changes from rainy to snowy will decrease over time, then, the figure II represents this situtation.
2)The number of fish caught per hour on a bad fishing day will have an almost constant function (since it was a bad day for fishing) thus, the figure V models this situation.
3)The total amount of rain that falls on a rainy day increases over time. Therefore, the figure IV can be used to represent this situation.
J and K are supplementary angles. If mK is 68°, what is the measure of J
J and K are supplementary angles. If m ∠K is 68°, what is the measure of J.
________________________________________________
The sum of supplementary angles is 180º
∠ J + ∠K = 180º
∠ j = 180º - 68º
∠ j = 112º
________________________
Answer
∠ j = 112º
Which of the following circumstances would likely make the quadratic formula, completing the square, or factoring the best method for solving a quadratic equation?
THE LIFETIME OF A BATTERY USED IN A SMOKE ALARM IS NORMALLY DISTRIBUTED WITH A MEAN OF 4,000 HOURS AN A STANDARD DEVIATION OF 600 A. FIND THE % OF BATTERIES THAT WILL LAST BETWEEN 4120 AND 4720 HOURS? B.IF 500,000 BATTERIES ARE PRODUCED HOW MANY WILL LAST UP TO 4600 HOURS?
A) 30.6%
B) 420,500 batteries
Explanations:A) First, we need to convert the range of number of hours to z-scores, this can be expressed as:
[tex]z=\frac{x-\overline{\mu}}{\sigma}[/tex]where
µ is the mean value
σ is the standard deviation
If the number of hours is 4120 hours, then the z-score will be;
[tex]\begin{gathered} z_1=\frac{4120-4000}{600} \\ z_1=\frac{120}{600} \\ z_1=0.2 \end{gathered}[/tex]If the number of hour is 4720 hours, then the z-score wil be;
[tex]\begin{gathered} z_2=\frac{4720-4000}{600} \\ z_2=\frac{702}{600} \\ z_2=1.2 \end{gathered}[/tex]The equivalent z-score will be;
[tex]0.2Find the equivalent probability[tex]\begin{gathered} P(0.2Hence the percentage of batteries that will last between 4120 and 4720 hours is 30.6%B) In order to determine the total batteries that will last up to 4600 hours if the there are 500,000 batteries, we will have;
[tex]\begin{gathered} z=\frac{4600-4000}{600} \\ z=\frac{600}{600} \\ z=1 \end{gathered}[/tex]Such that;
[tex]P(z<1)=0.8413=84.13\%[/tex]Find the required number of batteries
[tex]\begin{gathered} Total\text{ batteries<}0.8413\times500,000 \\ Total\text{ batteries}<420650batteries \\ Total\text{ batteries}=420,500 \\ \end{gathered}[/tex]Since 420,500 is less than the calculated, hence the total batteries that will last up to 4600 hours is 420,500 batteries
One of the Boston Red Sox's player has the following stats thus far this season. He has been to bat (at-bat) 619 times and had 190 hits, that consisted of 50 doubles, 4 triples, and 31 homeruns. What is his slugging Avg?
Answer:
His slugging average is 0.551.
Step-by-step explanation:
Slugging average:
Sum of:
Singles multiplied by 1.
Doubles multiplied by 2.
Triples by 3.
Home runs by 4.
Divided by:
Number of at bats.
This player:
190 hits(singles + doubles + triples + homeruns)
His number of singles is:
190 - (50+4+31) = 190 - 85 = 105
His slugging average is given by:
[tex]S=\frac{1\ast105+2\ast50+3\ast4+4\ast31}{619}=\frac{105+100+12+124}{619}=0.551[/tex]His slugging average is 0.551.
Find the slope of each line.y=-5x – 1can you help me solve this
y=-5x – 1
To find the slope y=-5x – 1
we will compare it with the standard slope -intercept equation
which is y=mx + b
where m is the slope and b is the intercept
comparing the two, m=-5
Hence the slope = -5
What will it cost to place baseboard around the region shown if the baseboard costs $0.55 per foot? No baseboard is needed for the 2-foot doorway.
Answer:
It will cost $19.25 to place the baseboard around the region
Explanation:
The total number of feet that need the baseboard is the perimeter of the region minus 2 ft for the door.
10 ft + 7 ft + (13 - 2) ft + 3 ft + 4 ft = 35 ft
Now the cost is $0.55 per foot; therefore, for 35 ft the cost will be
[tex]cost\text{ per foot }\times number\text{ of feet}=\frac{\$0.55}{ft}\times35ft=\$19.25[/tex]Hence, the cost to place baseboard around the region will be $19.25.
find the value of expression when a=1/3, b=9, c=5, d=10; expression is 3c + b^2 : 27a - d
3c + b^2 : 27a - d
Replace
c with 5
b with 9
a with 1/3
d with 10
And solve:
3 (5) + 9^2 : 27(1/3) - 10
Use PEMDAS to solve in order.
First exponents:
3 (5) + 81 : 27 (1/3) -10
Then multiplications and divisions:
15 + 81 : 9 -10
15+ 9-10
Then add and subtract
14
Which of the following is the point and slope of the equation y+2=(x-8)
Answer:
y=x-10
Step-by-step explanation:
y+2=(x-8)
y=x-8-2
y=x-10
you can also graph it on any graphing calculator to get the same answer
A track runner ran for 15 minutes, walked for 15 minutes, ran for another 20 minutes, and then stretched in place for 10 minutes.Which graph describes the relationship between runner's total distance and time?
Note that:
When the track runner runs, he is expected to cover more distance than when walks
When he stretches his body, he is not expected to cover any distance because there is no motion when the body is stretched in place.
By carefully observing the graphs shown, the correct graph will be plotted in the format below:
Long distance for the first 15 minutes
Short distance for the second 15 minutes
Longer distance for the next 20 minutes
No distance covered in the last 10 minutes
Therefore, the only graph that describes the relationship between the runner's total distance and time is option B
Answer:
its A
Step-by-step explanation:
He rested and stretched for 15 minutes, aka he did not move
3. CHOCOLATE CHIP BROWNIE 1. Find the conversion factor to scale the Brownie recipe below for 4 servings and 80 servings using the formula: Desired yield - Original yield = Conversion Factor 2. Multiply each ingredient by the conversion factor. 3. When required, change ingredient measurements to use the best equivalent. For example, change 3 teaspoons to 1 tablespoon. 4. Ensure all new measurements are in whole numbers or fractions. INGREDIENT YIELD = 8 SERVINGS YIELD = 4 SERVINGS Conversion Factor = YIELD = 80 SERVINGS Conversion Factor = 1 1/2 Cup 1 tsp 1/4 tsp 1/2 tsp 1/8 tsp Flour Baking Powder Salt Cinnamon Nutmeg Egg Sugar 1 1/2 Cup
1. Conversion factor (k)=desired yield ÷ original yield
4 servings (k₄)
[tex]k_4=\frac{4}{8}=\frac{1}{2}[/tex]80 servings (k₈₀)
[tex]k_{80}=\frac{80}{8}=10[/tex]2. Once you have the convertion factors you have to multiply each ingredient by the corresponding k to get the correct amounts for the desired servings.
I'll start with all ingredients for 4 servings:
k₄=1/2
Flour
1 1/2 cups= 3/2 cups
[tex]\frac{3}{2}\cdot k_4=\frac{3}{2}\cdot\frac{1}{2}=\frac{3}{4}[/tex]For 4 servings you need 3/4 cups of flour
Baking powder
1 tbs * k₄=1 * 1/2= 1/2 tbs
For 4 servings you need 1/2 tbs baking powder
Salt
1/4tsp*k₄=1/4*1/2=1/8 tsp salt
Cinnamon
1/2 tsp * k₄= 1/2*1/2= 1/4 tsp cinnamon
Nutmeg
1/8 tst * k₄= 1/8*1/2= 1/16 tsp nutmeg
Egg
1 egg * k₄= 1 * 1/2= 1/2 Egg
Sugar
1/2cup *k₄= 1/2*1/2= 1/4 cup sugar
Buttermilk
1/2cup * k₄= 1/2*1/2= 1/4cup buttermilk
Vegetable Oil
1/4cup * k₄= 1/4*1/2= 1/8 cup vegetable oil
Vanilla
1/2tsp * k₄= 1/2*1/2= 1/4 tsp vanilla
Chocolate chips
3/4 cup * k₄= 3/4*1/2= 3/8 cup chocolate chips
I just want to know if I solved it right before I turn it in
Solving for x in the second equation, we get:
[tex]\begin{gathered} -3x+4y=-13 \\ -3x=-13-4y \\ x=\frac{-13}{-3}-\frac{4y}{(-3)} \\ x=\frac{13}{3}+\frac{4y}{3} \end{gathered}[/tex]Replacing x on the first one and solving for y, we get:
[tex]\begin{gathered} 2x+5y=1 \\ 2(\frac{13}{3}+\frac{4y}{3})+5y=1 \\ \frac{26}{3}+\frac{8y}{3}+5y=1 \\ \frac{8y}{3}+5y=1-\frac{26}{3} \\ \frac{23}{3}y=\frac{-23}{3} \\ y=-1 \end{gathered}[/tex]Finally, replacing y by -1, we get:
[tex]\begin{gathered} x=\frac{13}{3}+\frac{4}{3}\cdot(-1) \\ x=\frac{13}{3}-\frac{4}{3} \\ x=3 \end{gathered}[/tex]Answer: x = 3 and y = -1
There are 21 Women on the busThe ratio of Women to Men is 3:2How many people are on the bus all together?
Given:
Number of women in the bus = 21
Ratio of women to men = 3:2
Let's find the total number if people.
Where:
Total ratio = 3 + 2 = 5
To find the total number of people, we have:
[tex]\frac{3}{5}*x=21[/tex]Where:
x represents the total number of people.
To solve for x, multiply both sides by 5/3:
[tex]\begin{gathered} \frac{5}{3}*\frac{3}{5}x=21*\frac{5}{3} \\ \\ x=\frac{21*5}{3} \\ \\ x=\frac{105}{3} \\ \\ x=35 \end{gathered}[/tex]Therefore, the total number of people on the bus is 35.
ANSWER:
35 people
Find the vertex and write the quadratic function in vertex form (which our OpenStax textbook also calls the standard form).f(x)=x^2−10 x + 74 Give the vertex. Enter your answer as a point (a,b) .Vertex:Enter the coordinates of the vertex to write f(x) in vertex form:f(x)=(x− )^2+
We have the parabola equation in standard form:
[tex]y=ax^2+bx+c[/tex]and we need to convert it into a vertex form:
[tex]y=A(x-h)^2+k[/tex]In order to obtain it, we can note that
[tex]f(x)=x^2-10x+74[/tex]can be rewritten as
[tex]f(x)=(x-5)^2-25+74[/tex]this is because
[tex](x-5)^2=x^2-10x+25[/tex]From our last result, we have
[tex]f(x)=(x-5)^2+49[/tex]By comparing this result with the general vertex form, we can note that
[tex]\begin{gathered} A=1 \\ h=5 \\ k=49 \end{gathered}[/tex]Therefore, the equation in vertex form is given by:
[tex]f(x)=(x-5)^2+49[/tex]with vertex:
[tex](h,k)=(5,49)[/tex]A rectangular parking lot has an area of 2/3 square miles. The length of the parking lot is 1/6 of a mile. What is the width, in miles, of the parking lot ?
Answer
Width of the parking lot = 4 miles
Explanation
The area of a rectangle is given as
Area = L × W
where
L = Length of the rectangle = (1/6) mile
W = Width of the rectangle = ?
Area = (2/3) square miles
Area = L × W
(2/3) = (1/6) × W
[tex]\begin{gathered} \frac{2}{3}=\frac{1}{6}\times W \\ \frac{2}{3}=\frac{W}{6} \\ \text{Cross multiply} \end{gathered}[/tex]3W = (2)(6)
3W = 12
Divide both sides by 3
(3W/3) = (12/3)
W = 4 miles
Hope this Helps!!!
Find the missing coordinate given m = 4/3 and goes through the points (6, y) and (0,4).
Here's the slope formula we'll be using
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The two points will give us the numbers and variable that will replace the subscripted variables in the slope equation.
[tex]\begin{gathered} \frac{4}{3}=\frac{4-y}{0-6} \\ \frac{4}{3}=\frac{4-y}{-6} \\ \frac{4}{3}(-6)=\frac{4-y}{-6}(-6) \\ -8=4-y \\ -8-4=4-y-4 \\ -12=-y \\ y=12 \end{gathered}[/tex]coordinate: (6,12) and (0,4)
Michael pours 7/8 gallon of juice into a container, a week later 4/5 of that juice gone. what is the amount of juice, in gallons, that is gone?
The amount gone is 7/10 gallon
Here, we want to get the amount of juice in gallons that is gone
From the question, we are told that 4/5 of the poured amount is gone
Mathematically;
[tex]\frac{4}{5}\times\frac{7}{8}\text{ = }\frac{7}{10}\text{ gallon}[/tex]all you need is in the photo please answer fast
If you add two rational numbers, you will obtain a rational number. It means a+b is rational
If you substract an irrational from a rational, you will obtain an irrational number. It means a-c is irrational.
The product of two rational numbers is a rational number. It means a*b is rational.
The quotient of two irrational numbers can be both rational or irrational. It means c/d is rational or irrational.
If you add two irrational numbers, you will obtain a rational or an irrational number. It means c+d is rational or irrational.
As we said, the product of two rationals is a rational, but the product of a rational and an irrational is an irrational, it means, a*b*c is irrational.
Choy has $25 in his lunch account at school. He spends $3 each day to eat in the cafeteria, What is Choy's lunch account balance after two weeks of buying his lunch in the cafeteria?
First of all, we need to write a function or equation that describes the behavior of Choy's lunch account at school.
if x will be the numbers of days, y will be the amount of money in his account, then=
[tex]y(x)=25-3x[/tex]Now, after two weeks = 5*2 = 10 days, we need to find y(10) replacing x= 10 in the previous equation, like this:
[tex]\begin{gathered} y(x)=25-3x \\ y(14)=25-3(10) \\ y(14)=25-30 \\ y(14)=-5 \end{gathered}[/tex]Finally, the balance on his account is a debt of 5 dollars.
Point C(1,4) is reflected over the line x = 2. Write the coordinates of C'Point D(2,-10) is rotated 90° clockwise about the origin. Write the coordinates of D'Point E(2,-3) is translated using the rule (x,y) --> (x+2,y-2). Write the coordinates of E'
C' = (3,4)
2.- D = (2, -10)
D' = (-10, -2)
3.- E = (2, -3)
E' = (4, -5)
Which inequality is represented by this graph?5(0.1)(5,0)5-5O A. y >- x+1B. yy<- 6x +1C. 72-*x+1D. ys-x+1
We can see a graph representing an inequality. We also can see that we have two points (two coordinates) that lie on a line, and since we have a dotted line, we need to use an inequality symbol that does not take into account the values of the line, that is, we need to use < or >.
Now, to find the expression of the inequality on the graph, we need to proceed as follows:
1. Find the equation of the line using the given points: (0, 1) and (5, 0).
We can use the two-point form of the line to find the equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]And now we can label both points as follows:
• (0, 1) ---> x1 = 0, y1 = 1
,• (5, 0) ---> x2 = 5, y2 = 0
And we can substitute these values into the above equation:
[tex]\begin{gathered} y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1}) \\ \\ y-1=\frac{0-1}{5-0}(x-0) \\ \\ y-1=\frac{-1}{5}x \\ \\ y-1+1=-\frac{1}{5}x+1 \\ \\ y=-\frac{1}{5}x+1 \\ \end{gathered}[/tex]2. We need to use a test point to find the direction of the inequality. Since we can see that the point (0, 0) is part of the shaded part of the inequality, we can substitute this point in the line equation above as follows:
[tex]\begin{gathered} x=0,y=0 \\ \\ 0=-\frac{1}{5}(0)+1 \\ \\ 0<1 \\ \end{gathered}[/tex]And we can see that the inequality is of the form (<).
Therefore, in summary, the expression that represents the inequality is:
[tex]y<-\frac{1}{5}x+1[/tex](Option B).
Find the true value and round to three decimal places
Given:
[tex]\cos 53.75\text{ degr}ees[/tex]Asked: Find the trigonometric value.
ANSWER: 0.5913096484
Rounded to three decimal points = 0.591
A state park has two hiking trails, Buckeye Trail and Bigfoot Trail. Last month, Shelby hiked Buckeye Trail 3 times and Bigfoot Trail 4 times for a total of 22 miles. Samuel hiked Buckeye Trail 6 times and Bigfoot Trail 3 times for a total of 24 miles. If x represents the length of Buckeye Trail and y represents the length of Bigfoot Trail, the situation can be represented by the system below. Solve the system by using elimination.
The length of Buckeye Trail is 2 miles and the length of Bigfoot Trail is 4 miles.
How to calculate the equation?Let x represents the length of Buckeye Trail.
Let y represents the length of Bigfoot Trail.
Shelby hiked Buckeye Trail 3 times and Bigfoot Trail 4 times for a total of 22 miles. This will be:
3x + 4y = 22
Samuel hiked Buckeye Trail 6 times and Bigfoot Trail 3 times for a total of 24 miles. This will be:
6x + 3y = 24
3x + 4y = 22 ..... i
6x + 3y = 24 ..... ii
Multiply equation i by 3
Multiply equation ii by 4
9x + 12y = 66
24x + 12y = 96
Subtract
15x = 30
Divide
x = 30/15
x = 2
The length of Buckeye Trail is 2 miles.
The length of Bigfoot Trail will be:
3x + 4y = 22
3(2) + 4y = 22
6 + 4y = 22
4y = 22 - 6
4y = 16
Divide
y = 16/4
y = 4
The length of Bigfoot Trail is 4 miles.
Learn more about equations on:
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63. Find CD to the nearest tenth if point Cis at (12, -8) and point Dis at (5, 19).
Answer
CD - 27.9
Step-by-step explanation:
Point C = (12, -8) and Point D = (5, 19)
CD means the distance between point C and D
[tex]\begin{gathered} CD\text{ = }\sqrt[]{(x1-x2)^2+(y1-y2)^2} \\ \text{where x1 = 12, y1 = -8, x2 = 5, y2 = 19} \\ CD\text{ = }\sqrt[]{(12-5)^2+(-8-19)^2} \\ CD\text{ = }\sqrt[]{7^2+(-27)^2} \\ CD\text{ = }\sqrt[]{49\text{ + 729}} \\ CD\text{ = }\sqrt[]{778} \\ CD\text{ = 27.9} \end{gathered}[/tex]Hence, CD IS 27.9
What term best describes 3x + 5?algebraic expressionvariablecoefficientnumeric expression
Answer:
Algebraic expression
Explanation:
Given the sum:
[tex]3x+5[/tex]• The ,letter x, is referred to as a ,variable,.
,• The ,number beside x, that is, 3 ,is referred to as a ,coefficient.
A combination of these two, 3x will give an algebraic term.
Thus, a sum of the algebraic term, 3x and the constant, 5 is best referred to as an algebraic expression.
7 friend used 1/4 cuos of flour in their cske recipe. How many cups of flour were used altogether? Expess your answer in a mixed number
1 3/4 cups of flour were used altogether
Explanation:Quantity used by each friend = 1/4 cups of flour
There are 7 friends
The total number of cups used all together:
[tex]\begin{gathered} =\frac{1}{4}\text{cups of flour }\times\text{ }7\text{ friends} \\ =\text{ 7/4} \end{gathered}[/tex]The total number of cups used all together = 7/4
In mixed fraction = 1 3/4 cups of flour were used altogether