Answer:
The area of a rectangle is 5/4
Step-by-step explanation:
Help pls!!!!!!
A family sized box of cereal with dimensions 3x9x12 inches costs $6, while the regular size with dimensions 2x8x9 inches costs $4.50. What is the difference in price per cubic inch?
Answer:
$0.01
Step-by-step explanation:
Family size rate (per cubic inch)
Volume of box = 3 x 9 x 12 = 324 in³Cost = $6Rate = 6/324 = 1/54 = $0.02 per cubic inchRegular size rate
Volume of box = 2 x 8 x 9 = 144 in³Cost = $4.50Rate = 4.50/144 = 1/32 = $0.03 per cubic inchDifference in price
$0.03 - $0.02$0.01Volume of family sized box
LBH3(9)(12)27(12)324in³Price per inch
6/324=0.02$/inVolume of regular size
2(8)(9)144in³Price per in
4.5/144=0.03$/inDifference:-
|0.02-0.03|=0.01$
8. (06.04 MC)
Calculate the area of triangle ABC with altitude BD, given A (-6,0), B (0,0), C (0,6), and D (-3,3). (5 points)
18 square units
21 square units
9 square units
18.5 square units
Check the picture below.
the area of the triangle whose base is AC and height is BD, is the same area of the triangle whose base is AB and altitude is BC, namely
[tex]A=\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{6})\implies 18[/tex]
Fractional Area
What fraction of the square's total area
is shaded?
Answer:
7/32
Step-by-step explanation:
Cube Root Values
What two whole numbers does 81 lie between
Answer:
between 4 and 5
Step-by-step explanation:
consider perfect cubes either side of 81 , that is
64 < 81 < 125 , then
[tex]\sqrt[3]{64}[/tex] < [tex]\sqrt[3]{81}[/tex] < [tex]\sqrt[3]{125}[/tex] , that is
4 < [tex]\sqrt[3]{81}[/tex] < 5
The function h(t) = -4t^2 + 20t represents the height (in feet) of an athlete t seconds after pole vaulting. after how many seconds does the athlete reach his or her maximum height?
Answer:
2.5 seconds.
Step-by-step explanation:
h(t) = -4t^2 + 20t
= -4(t^2 - 5t)
Convert to vertex form by completing the square:
h(t) = -4[(t - 2.5t)^2 - 6.25]
= -4(t - 2.5)^2 + 25 <--------- vertex form
So the vertex is at the point (2.5, 25).
So the athlete reaches the maximum height ( of 25 feet), after 2.5 seconds.
Help, please the product of x and y
[tex]xy \\\\=\left(\log_{5\sqrt 5} ~125 \right)\left(\log_{2\sqrt 2} ~64 \right)\\\\=\left(\log_{5\sqrt 5} ~5^3 \right)\left(\log_{2\sqrt 2}~2^6 \right)\\\\=\left(3\log_{5\sqrt 5} ~5 \right)\left(6\log_{2\sqrt 2} ~2 \right)\\\\=\left( 18 \cdot \dfrac{\ln5}{\ln\left(5\sqrt 5\right)} \cdot \dfrac{\ln 2}{ \ln \left( 2 \sqrt 2 \right)}\right)\\\\[/tex]
[tex]=\left( 18 \cdot \dfrac{\ln5}{\ln\left(5^{\tfrac 32}\right)} \cdot \dfrac{\ln 2}{ \ln \left( 2^{\tfrac 32} \right)}\right)~~~~~~~~~~~;\left[\sqrt a = a^{\tfrac 12}~~ \right]\\\\=\left( 18 \cdot \dfrac{\ln5}{\tfrac 32\ln5^} \cdot \dfrac{\ln 2}{\tfrac 32 \ln 2 }\right)\\\\\\=18 \cdot \dfrac 23 \cdot \dfrac 23 \\\\=\dfrac{72}9\\\\=8[/tex]
How far does the unicycle move if the wheel turns once?
Pierre enters a 100m unicycle race. How many times must the wheel rotate completely in order for Pierre to travel 100m?
The unicycle moves a distance of 251.20cm if the wheel turn once and the wheel must rotate 32 times to cover a distance of 100m
Circumference of a circleThe formula for calculating the circumference of a circle is given as:
C = 2pi r
r is the radius of the circle
a) r = 80/2 = 40cm
C = 2(3.14)(40)
C = 251.20 cm
Hence the unicycle moves a distance of 251.20cm if the wheel turn once
b) Number of revolution * 2pi r = distance covered
n * 2(3.14)(50) = 10000
314n = 10000
n = 10000/314
n =32
Hence the wheel must rotate 32 times to cover a distance of 100m
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What are the values of a and b? a = 14, b = 6 a = 14, b = 8 a = 17, b = 6 a = 17, b = 8
The value of a and b given that the opposite side are equal are 17 and 6 respectively
Properties of a kiteThe kite is a quadrilateral with 4 sides and the opposite side of the side are equal. If they are, then;
2a - 4 = 30
2a = 34
a = 17
Similarly
3b+6 = 24
3b = 18
b = 6
Hence the value of a and b given that the opposite side are equal are 17 and 6 respectively
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A date is picked at random on the calendar for april. what is the probability that the date chosen will be on a two digit odd number
Answer:
1/3
Step-by-step explanation:
That is the simplified version of the number of all the double-digit odd days (11,13,15,17,21,23,25,27,29), 10, over the total number of days in April, 30
10/30=1/3
40) through: (-5, 2), slope
1
5
Answer:
y = 1/5x + 3
Step-by-step explanation:
y = mx + b
m: slope = 1/5
b: y - intercept
(x, y): (-5, 2)
2 = 1/5(-5) + b
2 = -1 + b
add 1 to both sides to get b alone
2 + 1 = -1 + b + 1
3 = b
Solve 6^x+2 = 10 for x using the change of base formula
Answer:
[tex]x\approx-0.7149[/tex]
Step-by-step explanation:
[tex]\displaystyle 6^{x+2}=10\\\\\log_6(6^{x+2})=\log_6(10)\\\\x+2=\frac{\log(10)}{\log(6)}\\\\x+2\approx1.2851\\\\x\approx-0.7149[/tex]
Recall that the change of base formula is [tex]\displaystyle \log_a(b)=\frac{\log(b)}{\log(a)}[/tex]
PLEASE HELP WILL MARK BRAINLIEST WITH 100 POINTS
What is the best way to describe the center of the data represented in this line plot?
Select from the drop-down menus to correctly complete the statement.
The
median
mean
is
1 inch
1.5 inch
1.8 inch
2 inches
Line plot titled Daily Rainfall. The number line is labeled Number of inches. There are 3 dots above 0, 3 dots above 1, 1 dot above 2, 1 dot above 3, 1 dot above 4, and 1 dot above 6.
.
Answer:
Mean = 1.8 in
Step-by-step explanation:
MedianThe Median is the middle value when all data values are placed in order of size.
Ordered data values: 0, 0, 0, 1, 1, 1, 2, 3, 4, 6
As there is an even number of data values, the middle value is the mean of the middle two data values. Therefore, the Median = 1 in
MeanThe Mean is the sum of all data values divided by the total number of data values.
[tex]\implies \textsf{Mean}=\dfrac{0+0+0+1+1+1+2+3+4+6}{10}=1.8[/tex]
Therefore, the Mean = 1.8 in
ConclusionThe Median is a better measure of central tendency when the data includes outliers (data values that are far away from the majority), as it is not affected by those outliers. As there does not appear to be any outliers in this data set, the mean can be used to best describe the center of the data.
Therefore, the Mean = 1.8 in
A 13-foot ladder is leaning against a building, forming a right triangle.
The height where the ladder touches the building is seven feet more
than the distance from the base of the ladder to the building. At what
height does the ladder touch the building?
The height from the ground at which the ladder touched the building is 12feet.
What is a right-angled triangle?A right-angled triangle is a type of triangle that has three sides and one of its three angles as 90°.
Analysis:
The ladder length, height of the ladder from the ground, and the distance of the foot of the ladder from the foot of the building form a right angle triangle.
let x, be the distance from the foot of the building to the foot of the ladder.
x+7 = height of ladder from building to foot of building.
length of ladder = 13 feet
using Pythagoras, we have
[tex](13)^{2}[/tex] = [tex]x^{2}[/tex] + [tex](x+7)^{2}[/tex]
169 = [tex]x^{2}[/tex] + [tex]x^{2}[/tex] + 7x + 7x + 49
169 = 2[tex]x^{2}[/tex] + 14x + 49
2[tex]x^{2}[/tex] + 14x = 169-49
2[tex]x^{2}[/tex] + 14x = 120
divide through by 2
[tex]x^{2}[/tex] + 7x - 60 = 0
[tex]x^{2}[/tex] +12x -5x - 60 = 0
(x+12) -5(x+12) = 0
(x+12)(x-5) = 0
x = -12 or 5
Since measurement cannot be negative, therefore x = 5
Height the ladder touches the building is x+7 = 5+7 = 12 feet
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I need help. Please and thank you
Answer:
3/4
Step-by-step explanation:
Subtract 3 2/4 from 2 3/4
- Multiply 3 and 4 to get 12.
- Add 12 and 2 to get 14.
- Reduce the fraction 14/4 to lowest terms by extracting and canceling out 2.
- Multiply 2 and 4 to get 8.
- Add 8 and 3 to get 11.
- Least common multiple of 2 and 4 is 4. Convert 7/2 and 11/4 to fractions with denominator of 4
- Since 14/4 and 11/4 have the same denominators, subtract both by subtracting their numerators
- Subtract 11 from 14 to get 3
I need help! A flagpole casts a shadow 25 feet long and the angle of elevation of the sun is 72 degrees. Find the height of the flagpole to the nearest foot.
Answer:
From the diagram you can see that we have constructed a right triangle, with height A and base 15.Length of shadow = 15 feet.Height of flagpole = A.We know the angle of elevation is 40∘. Using this angle and the tangent ratio, we can find A.tan(40∘)=oppositeadjacent=A15∴tan(40∘)=A15Rearranging:A=15tan(40∘)By calculator:A=12.59 feet. ( 2 d.p.)
For any positive numbers a,b, and d, with b=1, logb a+logb d=
Answer the right answer is a
Which line is the best model for the data in the scatter plot?
Answer:
the top right (2) answer is probably what you'll want to go for, if this is incorrect then you have my deepest apologies
Step-by-step explanation:
A ring-shaped region is shown below.
Its inner diameter is 16 ft. The width of the ring is 2 ft.
it
16 ft
Find the area of the shaded region.
Use 3.14 for . Do not round your answer.
X5?
Answer:
Area = 213.52 sq.ft
Step-by-step explanation:
[tex]A_{s} =\pi (18)^{2} -\pi (16)^{2} =324\pi -256\pi =68\pi[/tex]
[tex]\pi =3.14[/tex]
[tex]A_{s} =68(3.14)=213.52sq.ft[/tex]
Hope this helps
Answer:
113.04 ft²
Step-by-step explanation:
The area of the ring can be found by multiplying its center-line length by its width.
__
The diameter of the circle that is the center-line of the ring is ...
16 ft + 2 ft = 18 ft . . . . center-line diameter
The length of the center-line is then ...
C = πd
C = 3.14(18 ft) = 56.52 ft
And the area of the ring is ...
A = LW = (56.52 ft)(2 ft) = 113.04 ft²
The shaded area is 113.04 square feet.
Find the radian measure of the central angle of a circle of radius 12 that intercepts an arc length 32.5. Round to the nearest hundredth.
An object is fired from a cannon. Its height after t seconds is given by the function
h(t)= 16t² + 128t + 140 feet. How high was the object after 2 seconds?
=
The object was
feet high.
Answer:
332 feet
Step-by-step explanation:
Height = h(2) = - 16(2^2) + 128t + 140 ( NOTE: I added the minus sign)
= 332 feet
The maximum height is 908 feet.For a parabola, h = ax^2 + bx + c, the vertex at point (h,t), is first found by the equation t = b / 2a, and then plugging that point into the equation to find h.
What is more about the problem?For a parabola, h = ax^2 + bx + c, the vertex at point (h,k), is first found by the equation t = b / 2a, and then plugging that point into the equation to find h.
Given the equation h = 16t^2 + 128t + 140, we know a = 16, b = 128, c = 140.
t = -b/2a
t = -(128) / 2(16)
t = -128 / 32
t = 4 seconds
let's plug in t=4 to our equation:
h = 16t^2 + 128t + 140
h = 16*(4)^2 + 128*(4)+ 140
h = 908ft
h = 908 feet
answer is that the maximum height is 908 feet.
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( i will give brainlist ) please help is the following equation linear, quadratic, exponential or none of these?
Answer:
exponential
Step-by-step explanation:
It is exponential because the variable is in the exponent
In a poll of Mr. Briggs’s math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.
This is not a valid conclusion because the data was not randomly collected from various classes in the school but from a particular class.
Collection of data for a research workThe collection of data for a research work should be done in such a way as to include a good number of the test subjects.
The sampling methods that can be used to gather better data include the following:
Random sampling,Cluster sampling, andSystematic sampling methods.These methods will ensure that a good number of the test subjects are included in the research work in order to form a valid conclusion.
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Use the given scale and determine the actual straight -line distance between East London and Bloemfontein
Answer:
Driving Distance : 569 KM and 398 meters / 353.8 miles.
Straight Line Distance : 467 KM and 700 meters / 290.6 miles.
Travel time : 11 hours and 19 minutes.
Direction and bearing : South side, 159 degree.
Step-by-step explanation:
17. Write interval notation for the given graph.
Answer:
D
Step-by-step explanation:
The interval notation for the graph :
-5 ≤ x ≤ 7[5, 7]The mosaic had a 7 × 7 array of different color square tiles. If each tile is 3
1
2
ft long, what is the area of the whole mosaic
Answer:
441 square feet.
Step-by-step explanation:
Area = length times width. Both length and width are 21 feet (3×7).
You flip a coin and then roll a 6-sided number cube (a die).
Find the probability of rolling a four and getting heads.
How many different combinations of six people can sit in four chairs?
assume one person sits in each chair.
Answer:
15Step-by-step explanation:
the number of combinations of 4 people we can form from 6 is :
[tex]C^{4}_{6}=\frac{6!}{4!\left( 6-4\right) !} = 15[/tex]
What is the solution to 2x²+8x=x²-16?
Ox=-4
Ox=-2
Ox=2
Ox=4
Answer:X is equal to -4 twice
Step-by-step explanation:
The solution to the equation 2x² + 8x = x² - 16 is x = -4.
Option A is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To solve the equation 2x² + 8x = x² - 16, we first simplify it by moving all the terms to one side:
2x² + 8x - x² + 16 = 0
Simplifying further, we get:
x² + 8x + 16 = 0
This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 8, and c = 16.
We can solve this equation by factoring it:
(x + 4)(x + 4) = 0
This gives us two solutions:
x + 4 = 0 or x + 4 = 0
x = -4 or x = -4
Therefore,
The solution to the equation 2x² + 8x = x² - 16 is x = -4.
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19. Find the x- and y-intercepts of the equation -x + 2y = 8. Write your answers as ordered pair.
Yo anyone from United States I gotta question
what's your question question question
