Answer:
5 buses
Step-by-step explanation:
You add all the students up to get 168, because that's the total number of students, and divide it by 36. The buses can only carry 36 people, so you will need 4.666 buses, but you can't have 0.666 of a bus, so you will need 5 buses to fit everyone.
Use the slope formula to find the slope of the line through the points (1, -2) and (-2,8).
Sorn thatic in
Answer:
Step-by-step explanation:
(8 + 2)/(-2 - 1)= -10/3
The revenue from the sale of specialty golf hats is given by the function R(x) = 31x, where x is the number of hats sold.
a. What is R(200)? Interpret this result
b. What is the revenue from the sale of 3000 hats? Write this in functional notation.
a. R(200) =
Answer:
[tex]R(200) = 6200[/tex]
[tex]R(3000) = 93000[/tex]
Step-by-step explanation:
Given
[tex]R(x) = 31x[/tex]
Solving (a): R(200)
[tex]R(x) = 31x[/tex]
Substitute 200 for x
[tex]R(200) = 31 * 200[/tex]
[tex]R(200) = 6200[/tex]
This means that the revenue from 200 hats is 6200
Solving (b): Revenue from 3000 hats
[tex]R(x) = 31x[/tex]
Substitute 3000 for x
[tex]R(3000) = 31 * 3000[/tex]
[tex]R(3000) = 93000[/tex]
The above represents the functional notation and the revenue sale is 93000
Which expressions are equal to z+(z+6)
Answer:
2(z+3)
Step-by-step explanation:
2z+6
take out the 2: 2(z+3)
A linear correlation scatterplot is also a direct proportionality. True or False
Answer: False
Step-by-step explanation: A linear correlation scatter plot is one which is aimed at establishing a graphical view of the relationship between two quantitative variables. A linear correlation scatter plot could either be positive which is depicted by a positive gradient which infers direct proportionality, this means an increase in variable A results in increase in variable B while a decrease in variable A results in decrease in variable B. Similarly, it could also exhibit a negative gradient which infers a inverse proportionality meaning a decrease in one variable leads to increase of the other and vice-versa. Hence, a linear scatterplot does not only exhibit direct proportionality.
Which set of points are NOT collinear?
A
B
D
A and E
E and B
OD and B
OC and A
Given: mAngleTRV = 60° mAngleTRS = (4x)° Prove: x = 30 3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees. What is the missing reason in step 3?
Answer:
the answer is angle addition postulate
Step-by-step explanation:
Given the proof for x = 30, the missing reason in step 3 is: angle addition postulate
What is Angle Addition Postulate?Angle addition postulate states that if D is the interior of ∠ABC, therefore, the sum of the smaller angles equals the sum of the larger angle, which is: m∠ABD + m∠DBC = m∠ABC.
The given diagram as shown in the image attached below alongside the proof of x = 30.
T is the interior of straight angle ∠VRS.
m∠VRS = 180° (straight line angle)
Therefore, based on the angle addition postulate, m∠TRS + m∠TRV = 180°.
Thus, given the proof for x = 30, the missing reason in step 3 is: angle addition postulateLearn more about angle addition postulate on:
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Seven times the sum of a number and 2 equals 5
Answer: The number is -9/7
Step-by-step explanation:
The statement can be expressed by the equation
7(n + 2) = 5 where n is the number
Now solve for n
7(n+2) = 5 distribute on the left side
7n + 14 = 5
-14 -14
7n = - 9
n = -9 /7
The costs per load (in cents) of 47 dish-washing detergents tested by a consumer organization are shown here. Find the standard deviation of the sample.
Xavier caught a football and ran for eight yards before being pushed 17 yards backward.
Which equation correctly shows his change in yardage?
А
8 + (-17) = -9
-17 + (-8) = -25
B
С
17 + (-8) = 9
D
8 + 17 = 25
Answer:
Answer A
Step-by-step explanation:Option B is saying that he went back 8 yards and was pushed even farther. Option C is saying he ran foward 17 yards and got pushed back 8. Option D is saying he got pushed foward 17 yards.
Option A is saying that he ran 8 yards and then lost 17 by getting pushed back.
f(x) = -x² – 10x + 16
Find f(-7)
Answer:
-5
Step-by-step explanation:
or, f(x) = -x^2+10x+16
or, f(7) = (-7)^2+10*-7+16 (-7*-7=49)
=49-70+16
=65-70
=-5
Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane
Answer:
(a) (x - 3)² + (y + 4)² + (z - 5)² = 25
(b) (x - 3)² + (y + 4)² + (z - 5)² = 9
(c) (x - 3)² + (y + 4)² + (z - 5)² = 16
Step-by-step explanation:
The equation of a sphere is given by:
(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ---------------(i)
Where;
(x₀, y₀, z₀) is the center of the sphere
r is the radius of the sphere
Given:
Sphere centered at (3, -4, 5)
=> (x₀, y₀, z₀) = (3, -4, 5)
(a) To get the equation of the sphere when it touches the xy-plane, we do the following:
i. Since the sphere touches the xy-plane, it means the z-component of its centre is 0.
Therefore, we have the sphere now centered at (3, -4, 0).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;
[tex]d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}[/tex]
[tex]d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}[/tex]
[tex]d = \sqrt{(0)^2+ (0)^2 + (-5)^2}[/tex]
[tex]d = \sqrt{(25)}[/tex]
d = 5
This distance is the radius of the sphere at that point. i.e r = 5
Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 5²
(x - 3)² + (y + 4)² + (z - 5)² = 25
Therefore, the equation of the sphere when it touches the xy plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 25
(b) To get the equation of the sphere when it touches the yz-plane, we do the following:
i. Since the sphere touches the yz-plane, it means the x-component of its centre is 0.
Therefore, we have the sphere now centered at (0, -4, 5).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;
[tex]d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}[/tex]
[tex]d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}[/tex]
[tex]d = \sqrt{(-3)^2 + (0)^2+ (0)^2}[/tex]
[tex]d = \sqrt{(9)}[/tex]
d = 3
This distance is the radius of the sphere at that point. i.e r = 3
Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 3²
(x - 3)² + (y + 4)² + (z - 5)² = 9
Therefore, the equation of the sphere when it touches the yz plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 9
(b) To get the equation of the sphere when it touches the xz-plane, we do the following:
i. Since the sphere touches the xz-plane, it means the y-component of its centre is 0.
Therefore, we have the sphere now centered at (3, 0, 5).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;
[tex]d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}[/tex]
[tex]d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}[/tex]
[tex]d = \sqrt{(0)^2 + (4)^2+ (0)^2}[/tex]
[tex]d = \sqrt{(16)}[/tex]
d = 4
This distance is the radius of the sphere at that point. i.e r = 4
Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 4²
(x - 3)² + (y + 4)² + (z - 5)² = 16
Therefore, the equation of the sphere when it touches the xz plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 16
By using the general sphere equation and what we know about planes, we will get:
a) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2b) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2c) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2.General sphere equation.The general sphere of radius R centered in the point (a, b, c) is given by:
(x - a)^2 + (y - b)^2 + (z - c)^2 = R^2
If we want a sphere centered in (3, -4, 5) we will have:
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = R^2
a) We want the sphere to touch the xy-plane, (with z = 0) then the radius must be at least equal to the z-component of the point, so we have R = 5, then the equation is:
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2
b) This time is the yz-plane, so the radius must be equal to the x-component.
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2
c) Finally, the xz-plane, this time the radius must be equal to the y-component.
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2
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Rank the items from 1 to 4 based on their unit prices.
Use the drop-down menus to label the least expensive
item per pound with "1" and the most expensive item
per pound with "4."
Avocados:
Broccoli:
Carrots:
Onions:
Answer:Avocados:4
Broccoli:3
Carrots:2
Onions:1
Step-by-step explanation:I did the question it is correct.
*!* find the area and perimeter of the shapes below.
Answer:
a: 15 in
b:210 cm
c: 21 yds
Step-by-step explanation:
a: to find the area of a triangle multiply the base and the height, then divide the result by two.
b: to find the area of a trapezoid, multiply the median ( the point where the opposite corners cross) and the height.
c: to find the area of a parallelogram, multiply the lenght and the height.
Hope this helps!
Point T is on line segment SU. Given ST 2x + 1, SU = 4x, and
TU = 5x 4, determine the numerical length of ST.
Answer:
Step-by-step explanation:
3
what is 3/2 (7/3n +1)= 3/2
The question is Find the area.
Answer:
the area is 9in^3
Step-by-step explanation:
the formula for area of a triangle is 1/2bh, so it's 1/2 x 7.2 x 2.5
The vertical intercept of the line will always be a snap point.
A. True
B. False
Answer:
False because the vertical intercept is not always a snap point.
Step-by-step explanation:
In a line graph, the vertical intercept of a line will not always be a point snap. This is because snap points rest on nodes and are used to define boundary or shape of objects in a line graph. So in a case whereby the intercept of the line doesn't rest on a node that defines the boundary or shape of the object, then the vertical intercept may not be a snap point.
False
A vertical intercept is a point where a line crosses the vertical axis, or [tex]\boldsymbol{y-}[/tex]axis.
The vertical intercept of a line in a line graph is not always a snap point. Snap points are used to define the boundary or shape of objects in a line graph, rely on nodes. In the event when the line's intercept does not rest on a node that defines the object's boundary or shape, the vertical intercept may not be a snap point.
False, the vertical intercept of the line may not always be a snap point.
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Please answer this correctly without making mistakes
She will most likely finish graduation portraits.
I'm not to sure so try not to pick my answer.
|5-x|-|x+8|, if x>5
Answer:
just do it on ur caslc im pretty sure it would work
Step-by-step explanation:
what is 84.637 minus 28.56
Answer:
56.077
Step-by-step explanation:
Answer:
56.077
Step-by-step explanation:
i did it in my caculator lol :)
6. Use the data to find the following (Please show work)
2, 3, 5, 7, 8, 10, 11, 11, 13, 15, 17, 18
a. Mean
b. Median
C. Mode
d. Range
Answer:
1. [tex] \boxed{ \boxed{ \sf{mean = 10}}}[/tex]
2. [tex] \boxed{ \boxed{ \sf{median = 10.5}}}[/tex]
3. [tex] \boxed{ \boxed{ \sf{mode = 11}}}[/tex]
4. [tex] \boxed{ \boxed{ \sf{range = 16}}}[/tex]
Step-by-step explanation:
1. Given data : 2 , 3 , 5 , 7 , 8 , 10 , 11 , 11 , 13 , 15 , 17 , 18
Σx = 2 + 3 + 5 + 7 + 8 + 10 + 11 + 11 + 13 + 15 + 17 + 18 = 120
N ( total number of items ) = 12
Finding the mean
To find the mean, divide the sum of all the items by the number of items.
[tex] \boxed{ \sf{mean = \frac{Σx}{N} }}[/tex]
[tex] \dashrightarrow{ \sf{mean = \frac{120}{12} }}[/tex]
[tex] \dashrightarrow{ \sf{mean = 10}}[/tex]
Mean = 10
----------------------------------------------------------
2. Given data : 2 , 3 , 5 , 7 , 8 , 10 , 11 , 11 , 13 , 15 , 17 , 18
N ( total number of items ) = 12
Finding the position of median
[tex] \boxed{ \sf{median = { \frac{n + 1}{2} }^{th \: item}}} [/tex]
[tex] \dashrightarrow{ \sf{median = {( \frac{12 + 1}{2}) }^{th \: } item}}[/tex]
[tex] \dashrightarrow{ \sf{median = {( \frac{13}{2}) }^{th \: }item }}[/tex]
[tex] \dashrightarrow{ \sf{median = {6.5}^{th \: }}} [/tex] item
[tex] \sf{ {6.5}^{th} }[/tex] item is the average of 6 th and 7 th items.
[tex] \sf{∴ \: median = \frac{ {6}^{th}item + {7}^{th} item}{2}} [/tex]
[tex] \dashrightarrow{ \sf{median = \frac{10 + 11}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{median = \frac{21}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{median = 10.5}}[/tex]
Median = 10.5
-----------------------------------------------------------
3. The mode of a set of data is the value with the highest frequency.
Given data : 2, 3, 5, 7, 8, 10, 11, 11, 13, 15, 17, 18
Here, 11 has the highest frequency.
So, Mode = 11
----------------------------------------------------------
4. Highest number = 18
Lowest number = 2
[tex] \boxed{ \sf{range = highest \: number - lowest \: number}}[/tex]
[tex] \dashrightarrow{ \sf{range = 18 - 2}}[/tex]
[tex] \dashrightarrow{ \sf{range = 16}}[/tex]
Hope I helped!
Best regards! :D
Mrs. Krueger created the expression 4(h + 11) - 15 to estimate the number of hours each her students need to study each way to earn a certain grade average according to the expression how many hours per week does Lindsay needs to study if she wants to have an average of at least 90
Answer:
15.25 hours atleast.
Step-by-step explanation:
First rewrite the expression so it helps us find the answer.
4(h+11)-15=90
Distribute -> Substract from both sides -> Divide 61/4
[tex]4(h+11)-15=90\\4h+44-15=90\\4h+29=90\\4h=61\\61/4= 15.25h[/tex]
Mr. Crawford is ordering pizzas and breadsticks for a school pizza party and has a budget of $81, but no more. An order of breadsticks costs $7 and a pepperoni pizza costs $13. Write an inequality that represents the above situation if x represents the number of bread sticks and y represents the number of pizzas.
Answer:
7x + 13y [tex]\leq[/tex] $81
Step-by-step explanation:
The inequality that represents the situation given will be 7x + 13y ≤ 81.
From the information given, Crawford is ordering pizzas and breadsticks for a school pizza party and has a budget of $81, but no more and an order of breadsticks costs $7 while a pepperoni pizza costs $13.Therefore, the inequality that represents the situation given will be 7x + 13y ≤ 81.Read related link on:
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Write a number that is 90,000 greter than 8,304,088
7. Three cubes of edges x cm , 6 cm, and 8 cm are melted and recast into a bigger cube of
edge 12 cm , find the value of x?
Answer:
10 cm³
Step-by-step explanation:
Volume of a cube = (Side)³
Volume of bigger cube = (12)³
(12)³ = 1728 cm³
Volume of three cubes = (x)³ + (6)³ + (8)³ = 1728
(x)³ = 1728 - (6)³ - (8)³
(x)³ = 1000
x = ∛1000
x = 10 cm³
find the interval between: 8:40 pm and 9:30 am
Answer:
12 hours 50 minutes
Step-by-step explanation:
8:40 pm to 9:30 am
8:40 pm to 8:40 am = 12 hours
8:40 am to 9:30 am = 50 minutes
The interval between 8:40 pm and 9:30 am is 12 hours and 50 minutes
What is an Interval?
An interval is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers. This range includes all the real numbers between those two numbers.
Given data ,
Let the interval be denoted as [ a , b ] , where a is the start point and b is the final point
Now ,
a = 8:40 pm
b = 9:30 am
The interval can be calculated by ( b - a )
8:40 pm → 8:40 am = 12 hours
8:40 am → 9:30 am = 50 minutes
Therefore , total interval = 12 hours and 50 minutes
Hence , The interval between 8:40 pm and 9:30 am is 12 hours and 50 minutes
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Round each decimal to the place value stated and enter the value in the box a Round 3.892 to the nearest tenth. b. Round 5.424 to the nearest hundredth. c. Round 124.62 to the nearest whole number.
Answer:
A) [tex]\huge\boxed{3.9}[/tex]
B) [tex]\huge\boxed{5.42}[/tex]
C) [tex]\huge\boxed{125}[/tex]
Step-by-step explanation:
A) 3.892
To round off to nearest tenth, we'll see the digit in hundredths place. If it is greater than 5 or equal to 5, 1 will be added to the tenths place. If it's not, it will remain the same.
So, it will be like:
=> 3.9
B) 5.424
To round off to nearest hundredth, we'll see the digit in thousandths place. If it is greater than 5 or equal to 5, 1 will be added to the hundredths place. If it's not, it will remain the same.
So, it will be like:
=> 5.42
C) 124.62
To round off to nearest whole number, we'll see the digit in tenths place. If it is greater than 5 or equal to 5, 1 will be added to the ones place. If it's not, it will remain the same.
So, it will be like:
=> 125
Solve the linear equation. x - 3 = 7 x = ?
Answer: x = 10
Step-by-step explanation: You add 3 + 7 which equals 10. 10 minus 3 is 7.
what is 8 x 5 = 4 x _______
Step-by-step explanation:
[tex] \\ 8 \times 5 = 40 \\ 40 = 4 \times 10 \\ \\ 8 \times 5 = 4 \times 10[/tex]
A small apple weighs 4.5 ounces. if
it is divided into 4 equal Pieces, how
much dose each piece weighs
Answer:
1.125
Step-by-step explanation:
Each piece weighs 1.125 ounces
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that small apple weighs 4.5 ounces.
if it is divided into 4 equal Pieces then
Therefore, Weight of apple = 4.5 ounces
Total pieces = 4
Now Weight of 1 piece = 4.5 ÷ 4
= 1.125
Hence the answer is 1.125 ounces
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