Answer:
Statistics are incredibly important in real life. For example, we use statistics for weather forecasting. Probability (which is a form of statistics) is used by weather forecasters to figure out how likely it is that there will be rain, snow, sun, etc. on a given day in a certain area.
Step-by-step explanation:
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jhon and jack divided their math homework, jhon solved twice as many problems as jack
Answer:
If this is your question: john and jack divided there math homework.John solved twice as many problems as jack plus 1 more problem how many problems did each boy solve if there are 28 assigned problems?
Answer:
John: 19
Jack: 9
Step-by-step explanation:
Hope it helps! God bless!
I need the answer for the what if one
so you would ski down the mountain to the nearest foot is 2556.06ft
please help with this kenkenpuzzle
Answer:
it's a bit hard to see in green.
8. Given the following function, (a) find the vertex; (b) determine whether there is a maximum or a minimum value, and find the value; (c) find the range; and (d) find the intervals on which the function is increasing and the intervals on which the function is decreasing.
Answer:
Step-by-step explanation:
Parabola:
[tex]\sf f(x) =\dfrac{-1}{2}x^2+7x - 5\\\\a = \dfrac{-1}{2} \ ; b = 7 \ ; \ c = -5[/tex]
[tex]\sf x = \dfrac{-b}{2a}\\\\x =\dfrac{-7}{2*\dfrac{-1}{2}}\\\\ = \dfrac{-7}{-1}[/tex]
x = 7
Now, to find the y-value substitute this in the equation
[tex]\sf f(x) = \dfrac{-1}{2}*7^2+7*7-5\\\\ =\dfrac{-49}{2}+49-5\\\\ = \dfrac{-49}{2}+44\\\\ = \dfrac{-49}{2}+\dfrac{88}{2}\\\\= \dfrac{39}{2}[/tex]
[tex]\boxed{Vertex(7 ,\dfrac{39}{2})}[/tex]
b) The value of a is negative. So, the parabola is open down words and the maximum value is given by the y-coordinate of the Vertex.
[tex]\sf \boxed{Maximum \ value= \dfrac{39}{2}}[/tex]
[tex]\sf c) Range = [\dfrac{39}{2}, -infinity)[/tex]
Answer:
(a) (7,39/2)
(b) Maximum, 39/2
(c) y ≤ 39/2
(d) Increase when x < 7 and decrease when x > 7
Step-by-step explanation:
Given the parabola:
[tex]\displaystyle \large{f(x)=-\dfrac{1}{2}x^2+7x-5}[/tex]
( A ) Find the vertex
In order to find the vertex, let’s use calculus for this one. Recall the power rules for differentiation:
Power Rules
[tex]\displaystyle \large{f(x)=x^n \to f'(x)=nx^{n-1}}\\\\\displaystyle \large{f(x)=kx^n \to f'(x)=knx^{n-1} \quad \tt{(k \ \ is \ \ constant)}}\\\\\displaystyle \large{f(x)=k \to f'(x)=0 \quad \tt{(k \ \ is \ \ constant)}}[/tex]
Derivative Definition
Derivative f'(x) is a slope itself or rate of changes.Derive the parabola:
[tex]\displaystyle \large{f'(x)=-\dfrac{1}{2}(2)x^{2-1} + 7(1)x^{1-1} -0}\\\\\displaystyle \large{f'(x)=-x+7}[/tex]
Since vertex has slope = 0 —> e.g f'(x) = 0:
[tex]\displaystyle \large{0=-x+7}\\\\\displaystyle \large{-x=-7}\\\\\displaystyle \large{x=7}[/tex]
Substitute x = 7 in f(x):
[tex]\displaystyle \large{f(7)=-\dfrac{1}{2}(7)^2+7(7)-5}\\\\\displaystyle \large{f(7)=-\dfrac{1}{2}(49)+49-5}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+44}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+\dfrac{88}{2}}\\\\\displaystyle \large{f(7)=\dfrac{39}{2}}[/tex]
Therefore, the vertex is at (7,39/2)
( B ) Determine if max or min then find the value
Since the parabola opens downward then there only exists maximum value. The maximum value is the y-value of vertex at x-value of vertex. Henceforth:
There is maximum value but no minimum value and the maximum value is 39/2 at x = 7.( C ) Find range
For parabola, range is minimum value </≤ y </≤ maximum value. We know that parabola has maximum value of 39/2 but no minimum value so we can just ignore it then we’d have:
y ≤ 39/2 is our range[Note: < and > are for open-dot meaning the value will not be included —> e.g x > 4 means 4 isn’t included in.]
( D ) Find the interval when function is increasing and when it’s decreasing
For parabola, the function will increase only if f'(x) or slope > 0 and will decrease only f'(x) < 0.
We know, from part A that the derivative is:
[tex]\displaystyle \large{f'(x)=-x+7}[/tex]
Therefore, when f'(x) > 0 —> e.g -x + 7 > 0:
[tex]\displaystyle \large{-x+7 > 0}\\\\\displaystyle \large{-x > -7}\\\\\displaystyle \large{x < 7}[/tex]
When f'(x) < 0 —> e.g -x + 7 < 0:
[tex]\displaystyle \large{-x+7 < 0}\\\\\displaystyle \large{-x < -7}\\\\\displaystyle \large{x > 7}[/tex]
Therefore, the function will increase when x < 7 and will decrease when x > 7.
IN THE FIGURE BELOW LINES P AND Q ARE PARALLEL. WHAT DO YOU NOTICE
IREADY 50 POINTS!!!
Answer:
-> Supplementary
-> Add up to 180°
Explanation:
A straight line has a measurement of 180°. Supplementary angles are angles that, when added together, equal 180°.
Since angles 5 and 6 make up a straight line, we know they will add up to 180°.
Pyramid A has a volume of 60 mm3 and Pyramid B has a volume of 937.5 mm3. What is the ratio of their heights?
A pyramid is a polyhedron built by connecting a polygonal base and a point known as the top. The ratio of the height of pyramid A to pyramid B is 0.064.
What is a pyramid?A pyramid is a polyhedron built by connecting a polygonal base and a point known as the top. A lateral face is formed by the base edge and top of each triangle.
The volume of a pyramid is given by the formula,
Volume of the pyramid = (Length×Width×Height)/3
= (Area of base ×Height)/3
If the area of the base of the two pyramids is the same, then the ratio of the volume of the two pyramids will be,
[tex]\dfrac{\text{Volume of Pyramid A}}{\text{Volume of Pyramid B}} = \dfrac{60\rm\ mm^3}{937.5\rm\ mm^3}\\\\\\\dfrac{3 \times \text{(Area of base})_a \times h_a}{3 \times \text{(Area of base})_b \times h_b}= \dfrac{60}{937.5}\\\\\\\dfrac{h_a}{h_b} = 0.064[/tex]
Hence, the ratio of the height of pyramid A to pyramid B is 0.064.
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Determine the general solution for sin(x-30°) = cos 2 x
Sally has just finished her thirty-fifth year with her company and is getting ready to retire. during her thirty-five years, sally’s average annual salary was $45,603. how much can sally expect to receive from social security annually if she were to retire today? (assume she will receive 42% of her average annual salary.) a. $191.53 b. $1,915.33 c. $19,153.26 d. $191,532.60
Using proportions, the amount that Sally can expect to receive from social security annually is given by:
c. $19,153.26.
What is a proportion?A proportion is a fraction of a total amount, and this fraction can also represent a percentage of the total amount.
She is expected to receive 42% of her average annual salary of $45,603, hence, considering 0.42 is equivalent to 42%:
A = 0.42 x 45603 = $19,153.26.
Which means that option C is correct.
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A cube-shaped aquarium has edges that are 1.75 ft long. the aquarium is filled with water that has a density of 72" lb/f" "t" ^3.
(a) should the aquarium be placed on a table that can support a maximum weight of 150 lb? explain why or why not.
(b) would the density of the water change if the aquarium was only half full? explain.
Answer:
No and the density changes along with the weight.
Answer:
(a) No. The weight is more than 150 lb.
(b) No. Density is not a function of volume.
Step-by-step explanation:
The weight of the aquarium is the product of the volume and the density of the contents.
(a)The volume of the aquarium is the product of its dimensions:
V = LWH = (1.75 ft)(1.75 ft)(1.75 ft) = 1.75³ ft³ = 5.359375 ft³
The weight of its contents, at 72 lb/ft³ will be ...
(72 lb/ft³)(5.359375 ft³) = 385.875 lb
The aquarium should not be placed on the table. The weight of the aquarium is too great for the load limit of the table.
__
(b)The density of water is the ratio of its mass to its volume. Density does not change with depth or volume. It is essentially constant. (Water is considered to be virtually incompressible. Its density changes slightly with temperature,)
No, the density of the water would not change.
_____
Additional comments
The half-full aquarium would weigh about 385.875/2 lb ≈ 194 lb. This is still too heavy for the table.
The density of water is actually about 62.4 lb/ft³. We assume the extra 10 lb/ft³ might take into account the weight of the aquarium and any gravel or other non-water content.
I need help please I have a picture of the problem down below.
Answer:
Step 1: Create a net for the triangular prism by "cutting" two edges of the triangular faces and unfolding.
Step 2: Find the area of each triangle. Find the area of the rectangle.
Step 3: Add all areas from step 2 together. This is the surface area.
Step-by-step explanation:
What should I write for this?
Answer:
a. Solve the System of Equations. Show your work
solve the system using substitution. show all work
.
In a system of nonlinear inequalities, where and what is the feasible region?
Answer:
the region of the graph where the shaded regions of the graph of each inequality overlap, or where the regions intersect
Step-by-step explanation:
Calculate the surface area of the polyhedra
Mrs. Hanger is painting the following picture of an H to hang in the entryway of her home. She has made the following scale drawing as her model. The scale used on the drawing is 1:6.
As you can see, the "H" is going to be painted brick red in the center of a rectangular beige background. This means the distance from the "H" to the top of the picture will be the same as the distance from the "H" to the bottom of the picture. Similarly, the distance from the "H" to the left side of the picture will be the same as the distance from the "H" to the right side of the picture. Finally, each segment of the "H" will have the same width.
Mrs. Hanger decides to change the scale of her drawing from 1:6 to 1:4.
Is the new scale drawing larger or smaller than the original scale drawing? Use complete sentences to explain your reasoning.
What are the dimensions of the painting on the new scale drawing?
The percentage of the rectangle that will be beige is 15.5 percent
What is a rectangle?
A rectangle is a quadrilateral having the four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
The width of the "H" is 1/2 the distance form the top to the bottom of the "H" is 1/2
1/2 + 1/2 =
the side length of the "H" is 4
4 x 1/2 = 2
The demensions of the other 1/2 by 4 are the same, therefore,
2 + 2 = 4
The middle section is 1 by 1/2
1 x 1/2 = 1/2
The equation is 2 + 1/2 = 2 1/2
and converted to decimal form it is 4.5
The rectangle is 4 by 5
So 4 x 5 = 20
20 - 4.5 = 15.5 percent
Hence the percentage of the rectangle that will be beige is 15.5 percent.
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PLS HELP ILL MARK U BRAINLIST
Answer:
x = 17 degrees y = 3 units
Step-by-step explanation:
Since angle F and E are equal, sides DE and DF are equal and you now have an equilateral triangle
each angle is 60 degrees so 4x - 8 = 60 shows x = 17
since the sides are equal : 8y-3 = 6y+3 shows y = 3
Answer:
x = 17 , y = 4
Step-by-step explanation:
since EF and DF are congruent , then
8y - 5 = 6y + 3 ( subtract 6y from both sides )
2y - 5 = 3 ( add 5 to both sides )
2y = 8 ( divide both sides by 2 )
y = 4
--------
the triangle has 3 congruent angles , then
3(4x - 8) = 180 ( divide both sides by 3 )
4x - 8 = 60 ( add 8 to both sides )
4x = 68 ( divide both sides by 4 )
x = 17
A cylindrical pipe is 28m long.its internal radius is 3.5 and external radius is 5 cm calculate:
The volume in cm,of the metal used in making the pipe
The volume of water in litres that the pipe can hold when full,correct to one decimal place
The volume in cm 112098 cm³.
The volume of water in liters 112 liter.
What is volume of cylinder?The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder.
Given: height= 28m= 2800cm, internal radius= 3.5 cm, external radius = 5 cm.
Volume of cylinder
= πr²h
= 3.14(5²-3.5²)2800
=3.14*12.75*2800
=112098 cm³
Volume of water in liter is 112.098 or 112 liter.
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Does anybody know this? I keep getting the wrong answer. ABC~PRT AC=15 BC=12 and PT=6 find the ares of ABC if the area of PRT=24mm^2
Answer:
The area of triangle ABC is 60 mm^2
Step-by-step explanation:
x = the area of triangle ABC
15/6 * x/24
x=60
Answer:
(d) 150 mm²
Step-by-step explanation:
The scale factor between the triangles is the ratio of the lengths of corresponding sides. The area ratio is the square of the scale factor.
__
scale factorΔABC is larger than ΔPRT by the factor ...
AC/PT = 15/6 = 5/2
areaThe area of ΔABC is the square of this factor times the area of ΔPRT:
area ABC = (5/2)²×area PRT
area ABC = (25/4)×(24 mm²)
area ABC = 150 mm²
1) If the diameter of a circle is changed from 8 cm to 4 cm, how will the circumference change?
A) increases by a factor of 2
B) decreases by a factor of 2
C) increases by a factor of 4
D) decreases by a factor of 4
Answer:
the answer is B.
Step-by-step explanation:
the formula for circumference of a circle is [tex]\pi[/tex]×diameter=C
[tex]\pi[/tex]·8=25.13
[tex]\pi[/tex]·4=12.56
12.56·2=25.13
What is the distance between the two points?
please help me with this math question
Answer:
Min max median and q3 is correct, q2 should be 8.5
Combine the like terms to create an equivalent expression. 8k−5k
Answer:
3k
Step-by-step explanation:
8k and 5k are "like terms" because they have the same variable to the same degree. So because the are like terms they can be subtracted. Similarly to how 8-5 is 3,
8k - 5k is 3k
Which Angle measure must equal 52•
Answer:
c
Step-by-step explanation:
vertically opposite angles are always equal
here, the angle with the measure 52 degree and angle c are vertically opposite angles
so angle with the measure 52 degree = angle c
angle c equals to 52 degree
12. Select all the numbers that are greater than 1.
a.
23
b.
0.63
7
C.
1
-
5
5
d.
7
N
2
e.
w
Im
2.
f.
Answer:
its 23, (0.63 maybe), 7 ,5,5 that’s it
Step-by-step explanation:
Which best describes the three-dimensional figure that can be made from the net shown?
a triangular prism that might not have 4 congruent and equilateral triangles
a triangular pyramid that might not have 4 congruent and equilateral triangles
a triangular prism that must have 4 congruent and equilateral triangles
a triangular pyramid that must have 4 congruent and equilateral triangles
Answer:
Option C
Step-by-step explanation:
See here the net seems like a equilateral triangle
And another equilateral traingle is inscribed in itSo 4 equilateral trianglesHence option C
what is the solution of 9 (x-8) = 3 (4x-12)
() = Exponents The things in perenthacys are exponents
Solving as exponents
[tex]\\ \rm\Rrightarrow 9^{(x-8)}=3^{(4x-12)}[/tex]
[tex]\\ \rm\Rrightarrow 3^{2(x-8)}=3^{2(x-6)}[/tex]
[tex]\\ \rm\Rrightarrow 2(x-8)=2(x-6)[/tex]
[tex]\\ \rm\Rrightarrow 2x-16=4x-12[/tex]
[tex]\\ \rm\Rrightarrow -2x=4[/tex]
[tex]\\ \rm\Rrightarrow x=-2[/tex]
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
Given equation:
[tex]9^{x-8}=3^{4x-12}[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^{x-8}=3^{4x-12}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2(x-8)}=3^{4x-12}[/tex]
[tex]\implies 3^{2x-16}=3^{4x-12}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies 2x-16=4x-12[/tex]
Subtract 2x from both sides:
[tex]\implies 2x-16-2x=4x-12-2x[/tex]
[tex]\implies -16=2x-12[/tex]
Add 12 to both sides:
[tex]\implies -16+12=2x-12+12[/tex]
[tex]\implies -4=2x[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{-4}{2}=\dfrac{2x}{2}[/tex]
[tex]\implies x=-2[/tex]
help help help help help
Answer:
∠ T = 76°
Step-by-step explanation:
RSTU is a cyclic quadrilateral
the opposite angles of a cyclic quadrilateral sum to 180°
∠ T + ∠ R = 180°
∠ T + 104° = 180° ( subtract 104° from both sides )
∠ T = 76°
Find KE the answer is 40 I just need help getting to it.
Answer:
EK = 8
Step-by-step explanation:
Intersecting Chords Formula: a • b = c • d
BK * KD = EK * KC
4 * 10 = (x+1) * (x-2)
40 = x^2 +x-2x-2
40 = x^2 -x -2
0 = x^2 - x-2-40
0 = x^2 -x -42
Factor
0 = (x-7) (x+6)
Using the zero product property
x-7 = 0 x+6 =0
x=7 x=-6
X is not negative
x=7
EK = x+1
EK = 7+1
EK = 8
Find the measures of the interior angles of the triangle.
I really need help with this, it is due 10 pm tonight, if you can help thanks so much :)
Answer:
∠ A = 140° , ∠ B = 30° , ∠ C = 10°
Step-by-step explanation:
the sum of the 3 interior angles = 180°
sum the given angles and equate to 180
x - 5 + 2x + 140 = 180
3x + 135 = 180 ( subtract 135 from both sides )
3x = 45 ( divide both sides by 3 )
x = 15
then
∠ A = 140°
∠ B = 2x = 2 × 15 = 30°
∠ C = x - 5 = 15 - 5 = 10°
Answer:
Angle A = 140°Angle B = 30°Angle C = 10°Step-by-step explanation:
Find the measures of the interior angles of the triangle.
The sum of the interior angles of a triangle is 180°180 = 140 + 2x + x - 5
40 + 5 = 3x
45 = 3x
x = 45 : 3
x = 15°
-----------------------
check
180 = 140 + 2 * 15 + 15 - 5
180 = 180
the answer is good
---------------------------
Find the angles
140° = angle A
2x = 15 * 2
2x = 30° (angle B)
x - 5 = 15 - 5
x = 10° ( angle C)
-----------------------
check
140 + 30 + 10 = 180°
the answer is good
PLEASE HELP ILL MARK BRAINEST!!!!
Answer:
1, 6, 11, and 16 in that order
Step-by-step explanation:
every time the x value increases by 1, the f(x) value increased by 5
