Answer:
100000
Step-by-step explanation:
the largest five digit number is 99999
to round it to the nearest hundred you must look at the tens place to see if it is above or below 5
it is above 5 so your round up
because it is a nine it becomes 10
this goes down the line until you get
100000
that is your answer
Answer:
99,999
it is the answer!
Decay (calculus problem)
Answer:
Step-by-step explanation:
If the half-life is k days, then you have
(1/2)^(300/k) = 0.696
k = 573.788
makes sense, since 69.6% is greater than 50%
Now solve for t in
(1/2)^(t/573.788) = 1/3
t = 909.432 days
makes sense -- about 1.5 half-lives
6.5 in. 5 in 7.5 in. What is the total surface area of this prism in square inches?
6.5 in. 5 in 7.5 in. What is the total surface area of this prism in square inches?
we have that
the total surface area of a prism is equal to
SA=2B+Ph
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
Let
L=6.5 in
W=5 in
H=7.5 in
so
B=L*W=(6.5*5)=32.5 in2
P=2(L+W)=2(6.5+5)=23 in
H=7.5 in
therefore
SA=2(32.5)+23(7.5)
SA=237.5 in2
surface area is 237.5 square inchessee the attached figure to better understand the problem
the surface area is the area of its six rectangular faces
so
SA=2(6.5)8(5)+2((5)(7.5)+2(6.5)*(7.5)=237.5 in2
Robert has attended 32 out of 40 soccer practices this year. Based on his record of attendance, which is
the probability that Robert will attend soccer practice in the future?
Step-by-step explanation:
he attended 32 of 40.
that was a rate
32/40 = 4/5 = 0.8
if he keeps the same ratio, then the probability for him to attend any soccer practice in the future is 0.8.
K
Find the average rate of change of the function f(x) = 6x from x₁ = 0 to x₂ = 3.
The average rate of change is
(Simplify your answer.)
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How do you find the average rate of change of
f
(
x
)
=
2
x
2
+
1
on [x,x+h]?
Calculus Derivatives Average Rate of Change Over an Interval
1 Answer
Steve M
Feb 28, 2017
4
x
+
2
h
Explanation:
The average rate of change of a continuous function,
f
(
x
)
, on a closed interval
[
a
,
b
]
is given by
f
(
b
)
−
f
(
a
)
b
−
a
So the average rate of change of the function
f
(
x
)
=
2
x
2
+
1
on
[
x
,
x
+
h
]
is:
A
r
o
c
=
f
(
x
+
h
)
−
f
(
x
)
(
x
+
h
)
−
(
x
)
=
f
(
x
+
h
)
−
f
(
x
)
h
...
.
.
[
1
]
=
2
(
x
+
h
)
2
+
1
−
(
2
x
2
+
1
)
h
=
2
(
x
2
+
2
x
h
+
h
2
)
+
1
−
2
x
2
−
1
h
=
2
x
2
+
4
x
h
+
2
h
2
−
2
x
2
h
=
4
x
h
+
2
h
2
h
=
4
x
+
2
h
Which is the required answer.
Additional Notes:
Note that this question is steered towards deriving the derivative
f
'
(
x
)
from first principles, as the definition of the derivative is:
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
This is the function we had in [1], so as we take the limit as
h
→
0
we get the derivative
f
'
(
x
)
for any
x
, This:
f
'
(
x
)
=
h
→
0
4
x
+
2
h
=
4
x
this is a example
The figure below is a net for a triangular prism. What is the surface area of the triangular prism, in square feet?
The figure consists of,
A rectangle with dimension 15 ft by 7 ft.
Two triangles with base b = 7 ft and height h = 5 ft.
A rectangle with dimension 15 ft by 5 ft.
A rectangle with dimension 15 ft by 8.6 ft.
Determine the surface area of triangular prism.
[tex]\begin{gathered} A=15\cdot7+2\cdot\frac{1}{2}\cdot7\cdot5+15\cdot5+8.6\cdot15 \\ =105+35+75+129 \\ =344 \end{gathered}[/tex]So, surface area of triangular prism is 344 square feet.
Choose the expression that is equivalent to the one shown
1. Rewrite the expression to get the numerator and denominator with the same base:
[tex]\frac{(2^3)^{12}}{(2^2)^3}=\frac{2^{36}}{2^6}[/tex]2. Divide by leavinfg the same base and subtracting the exponents:
[tex]\frac{2^{36}}{2^6}=2^{36-6}=2^{30}[/tex]Write the result with base 4:
[tex]2^{30}=(2^2)^{30/2}=4^{15}[/tex]As you can see above any of the given expression is equivalent to the given expression.Answer: none of these-10+*+5> 7-5
3
3. Here is an inequality:
What value of x will make the two sides equal?
35 225
4
Fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is denominator?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. The denominator is simply the bottom number.
-10+*+5>7-5 justification
-10+*+5> 7-5
Step 1:
Multiply
-10 * 5 = -50.
Step 2:
Subtract:
7 - 5 = 2
the result of step No. 1 > the result of step No. 2
= -50 > 2 = No
The result:
-10 * 5> 7 - 5 = No
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Describe all of the transformations applied to the parent function f(x) = x² to sketch g(x) = 4(x – 2)² – 5
The transformations required are to shift the graph to the right by 2 units, shrink the graph by a factor of 4 and shift the graph downwards by 5 units.
The parent function given to us is f(x).The function f(x) equals x².We need to sketch the function g(x).The function g(x) equals 4(x – 2)² – 5.First of all, we need to graph x².Then, for the graph of (x – 2)², we need to shift the previous graph to the right by 2 units.Then, to obtain the graph for 4(x – 2)², we will shrink the graph by a factor of 4.Finally, to get the graph for 4(x – 2)² – 5, we will shift the graph in a downward direction by 5 units.Hence, we will obtain our final graph.To learn more about functions, visit :
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In a rectangle the base measures (x + 7), height (x + 2), area = 36 cm
Calculate perimeter, height and base.
The values are given as;
Perimeter = 26cm
Height = 4cm
Base = 9cm
How to determine the valueThe formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values into the formula, we have;
36 = (x +7)(x + 2)
Now, expand the bracket
36 = x^2 + 2x + 7x + 14
collect like terms
36 = x^2 + 9x + 14
Make into quadratic equation
x^2 + 9x + 14 -36 = 0
x^2 + 9x - 22 = 0
Factorize the equation
x^2 + 11x - 2x - 22 = 0
Factorize further
x(x + 11) - 2( x + 11) = 0
Then, x - 2 = 0, x = 2
or x + 11 = 0
x = -11
Height = x + 2 = 4cm
Base = x + 7 = 9cm
The formula for perimeter is expressed as;
Perimeter = 2( l +w )
Perimeter = 2( 4 + 9)
Perimeter = 2(13)
Perimeter = 26 cm
Hence, the values are 26cm, 4cm and 9cm respectively.
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It was recently estimated that females outnumber males by about three or two. If there are 1770 people in a county, how many of them are females?
GIVEN
1) Females outnumber males by 3 to 2.
2) There are 1770 people in the city.
SOLUTION
Let the number of males be x and the number of females y. Therefore, the total number of people can be written to be:
[tex]x+y=1770\text{ -----------(1)}[/tex]If there are 3 females for every 2 males, we have that:
[tex]\begin{gathered} \frac{y}{3}=\frac{x}{2} \\ \therefore \\ x=\frac{2y}{3}\text{ ----------(2)} \end{gathered}[/tex]We can substitute equation (2) into equation (1) and solve for y:
[tex]\begin{gathered} \frac{2}{3}y+y=1770 \\ \frac{2y+3y}{3}=1770 \\ 5y=1770\times3 \\ 5y=5310 \end{gathered}[/tex]Dividing both sides by 5, we have
[tex]y=1062[/tex]There are 1062 females in the county.
which measurement is closest to the volume of the container in cubic inches
The volume of a cylinder is given as;
[tex]\begin{gathered} Vol=\pi\times r^2\times h \\ r=3 \\ h=10.5 \\ \text{Vol}=3.14\times3^2\times10.5 \\ Vol=3.14\times9\times10.5 \\ \text{Vol}=296.73in^3 \end{gathered}[/tex]Therefore, from the options provided, the closest to the volume of the container is 296.88 cubic inches.
Option B is the correct answer
The volumes, in ml, of olive oil can be modeled by a normal distribution, with mean 508 mL and standard deviation 12 ml.. a. Find the probability that a randomly selected bottle has a volume less than 500 mL. Round your answer to 3 significant figures. b. The probability that a randomly selected bottle has a volume greater than v mL is 0.366. Find the value of v.
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Explain the normal distribution with an example?
One straightforward example of anything that has a normal distribution pattern is height: The majority of people are normal height, although there are nearly equal numbers of people who are taller or shorter than average and a very small (but roughly comparable) number who are either extraordinarily tall or extremely short.
The four properties of a normal distribution are visible here. The mean, median, and mode are all equal in normal distributions, which are symmetric, unimodal, and asymptotically distributed.
Add the mean to the x value in step 1. Subtract the difference from the standard deviation in step two. A value of 1380 has a z-score of 1.53. Thus, 1380 is 1.53 standard deviations away from the distribution's mean.
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solve for x. round to nearest tenth. angle DEF is an equilateral triangle. hyp is 24
Since the triangle DEF is an equilateral triangle and x is the height of this triangle, we can use the following formula for the height of an equilateral triangle:
[tex]h=\frac{l\sqrt[]{3}}{2}[/tex]Where 'l' is the length of the triangle side.
So, using l = 13, we have:
[tex]\begin{gathered} x=\frac{13\cdot\sqrt[]{3}}{2} \\ x=\frac{13\cdot1.73}{2} \\ x=11.2 \end{gathered}[/tex]So the value of x is 11.2
If f(x) = x^4 − x^3 + x^2 and g(x) = −x^2, where x ≠ 0, what is (f ⁄g)(x)?
The correct answer is
[tex](\frac{f}{g})(x)=-x^2+x-1[/tex]To solve this, first let's write the division:
[tex]f(x)=x^4-x^3+x^2,g(x)=-x^2\Rightarrow(\frac{f}{g})(x)=\frac{x^4-x^3+x^2}{-x^2}[/tex]Now we can factor out a x^2 on the top and the bottom of the expression:
[tex](\frac{f}{g})(x)=\frac{x^4-x^3+x^2}{-x^2}\Rightarrow(\frac{f}{g})(x)=\frac{x^2(x^2-x+1)}{x^2(-1)}[/tex]Now we can cancel out and divide by (-1), or the same thing, multiply by (-1):
[tex](\frac{f}{g})(x)=\frac{x^2(x^2-x+1)}{x^2(-1)}=-(x^2-x+1)=-x^2+x-1[/tex]Then the answer is (f/g)(x) = -x^2 + x - 1. That's the third option
use the image to find angles Q & U. explain your reasoning.
Solution
Given
[tex]\begin{gathered} m<3=45^0 \\ m<1=50^0 \\ m<6=135^0 \end{gathered}[/tex][tex]\begin{gathered} m<6\text{ = m<1 + m<2 + m<3 \lparen corresponding angles are equal\rparen} \\ 135=50+m<2+45 \\ 135=95+m<2 \\ m<2=135-95 \\ m<2=40^0 \end{gathered}[/tex][tex]\begin{gathered} mA rectangular carport has area 150 square feet. The height of the carport is five feet less than twice its length. Find the height and the length of the carport.
We are given that the area of a rectangle is 150 square feet. If "h" is the height and "l" is the length then the area is given by:
[tex]hl=150[/tex]We are also given that the height is 5 feet less than twice its length, this can be written mathematically as:
[tex]h=2l-5[/tex]Now we can replace the value of "h" in the equation for the area:
[tex](2l-5)l=150[/tex]Now we use the distributive property:
[tex]2l^2-5l=150[/tex]Now we have a quadratic equation that can be written as:
[tex]2l^2-5l-150=0[/tex]We can factor this equation to determine the values of "l". We multiply and divide by 2:
[tex]\frac{4l^2-5(2l)-300}{2}=0[/tex]Factoring in the numerator:
[tex]\frac{(2l-20)(2l+15)}{2}=0[/tex]Now we take common factor in the first parenthesis in the numerator:
[tex]\frac{2(l-10)(2l+15)}{2}=0[/tex]Simplifying:
[tex](l-10)(2l+15)=0[/tex]Now we set each factor to zero:
[tex]\begin{gathered} l_1-10=0 \\ l_1=10 \\ 2l_2+15=0 \\ l_2=-\frac{15}{2} \end{gathered}[/tex]We take the positive value, therefore, the length of the rectangle is 10 feet. Now we replace this value in the equation for the height.
[tex]h=2(10)-5[/tex]Solving we get:
[tex]\begin{gathered} h=20-5 \\ h=15 \end{gathered}[/tex]Therefore, the height of the rectangle is 15 feet.
7/8 ^2
Choose the correct expanded form for the following expression .
Evaluate 7/8^2
The correct expanded form for the following expression is 7/8 × 7/8.
What is expanded form?The division of numbers into their component ones, tens, hundreds, thousands, ten thousand, and so forth creates the expanded form of the number. The expanded version of the number is the sum of each digit times its place value, which is used to represent the number. A number is broken down to show the value of each of its digits in order to be written in expanded form. 144 would then be converted to 100 + 40 + 4 = 144. It can be used to compute sums as well. When a number is expanded to show the value of each digit, it is written in expanded form. The numerical value of each digit in the number we are writing is represented using extended form.
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Look at the following equation:
12,400 × [] = 1,240
What number should go in the box to make the equation true? (1 point)
1/10
1/100
10
100
3) Triangle ABC is dilated by a scale factor of 4 to form triangle A'B'C'. Wha-are the coordinates of vertex A'? Make sure that you enter the coordinatesin the form of (x, y) below. *Your answer
Answer
A' (-8, 4)
Explanation
When a figure, that is on the coordinates system is dilated (that is, enlarged or reduced) with respect to the origin, the new coordinates of its edges is simply a product of its old coordinates and the scale factor.
For this question, the coordinates of A is (-2, 1) and the dilation of the triangle ABC is by a scale factor of 4.
So, the new coordinates of A will be calculated thus
A (x, y) = A' (x × scale factor, y × scale factor)
A (-2, 1) = A' (-2 × 4, 1 × 4) = A' (-8, 4)
Hope this Helps!!!
Find the volume of this figure
Answer: 704 ft^3
Step-by-step explanation:
8 ft x 8 ft x 8 ft = 512 ft^3
(8 ft x 8ft x 9 ft)/3 = 192 ft^3
512 ft^3 + 192 ft^3 = 704 ft^3
Find the value of X and each arc measurex =mAD=mBC = mDC =mDBC=
The value of x can be calculated as,
[tex]\begin{gathered} \text{ summation of angles = 360}^{\circ} \\ 12x+90+(2x+5)+(17x-14)=\text{ 360}^{\circ} \\ 31x+95-14=360 \\ 31x=360-81 \\ 31x=279^{\circ} \\ x=\frac{279^{\circ}}{31} \\ x=9 \end{gathered}[/tex][tex]\begin{gathered} \text{mAD }=\text{ 12x} \\ =12\times9 \\ =108^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mBC}=(2x+5)^{\circ} \\ =(2\times9)+5 \\ =18+5 \\ =23^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mDC }=(17x-14)^{\circ} \\ =(17\times9)-14 \\ =153-14 \\ =139^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mDBC }=\text{ }(2x+5)^{\circ}+(17x-14^{})^{\circ} \\ =23^{\circ}+139^{\circ} \\ =162^{\circ} \end{gathered}[/tex]Use the figure to the right to name each of the following.1. A line2. A plane
ANSWER and EXPLANATION
We want to name a line and a plane.
LINE
In naming a line, we use two lettters. The two letters are the letters at the beginning and the end of the line.
Now, from the diagram, we have the following lines:
- nY
- Xm
- Zl
PLANE
A plane is made up of two lines intersecting one another.
In naming a plane, three letters are used, with the letter at the intersection in the middle.
The planes in the diagram are:
- mYn plane
- lRm plane
If f(x) = -2x^2 + 6 and g(x) =3xm evaulate the expressions below:
a. f(-1) + g(4)
b. 2g(2) - 7
Answer:
a
Step-by-step explanation:
The side view of a tire resembles a doughnut. If the inner diameter is 11.0 in. and the out diameter is 25.0 in., what is the area (in square inches) of the side of the tire?
If the side view of a tire resembles a doughnut. If the inner diameter is 11.0 in. and the out diameter is 25.0 in., Then area of the side of tire is 92237.5 inches.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
A doughnut is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
A doughnut has two circles. One circle with in the other circle.
The diameter of inner circle is 11.
So radius of inner circle is 5.5 inches.
The diameter of outer circle is 25 inches.
The outer circle add diameter of inside circle.
25+11=36 inches.
The radius of outer circle is 18 iches.
The area of doubtnut
Area of big circle - Area of small circle or inner circle
Area of doubtnut= πR²-πr²
R outer radius= 18
r inner radius =5.5
Area of doubtnut= 3.142 (R²-r²)
=3.142(18²-5.5²)
=3.14(324-30.25)
=3.14(293.72)
=92237.5 inches
Hence the area of the side of the tire is 92237.5 inches
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The slope-intercept equation of a line is y= 4x-1. What is the slope of the line?
OA. The slope is 4.
OB. The slope is -4.
OC. The slope is -1.
OD. The slope is 1.
A candy stand sells lollipops, gumballs, and chocolates. The gumballs cost 5 cents more than the chocolates. The lollipops cost twice as much as the chocolates. A particular handful containing 3 gumballs, 2 lollipops, and 7 chocolates costs $2.11. What is the cost of each item?
The cost of lollipops, gumballs, chocolate is $ 0.268, $0.184, $0.134
What is an equation?
An equation is a formula that describes the equality between two expressions, by connecting them with the equals sign '='.
Let the cost of lollipops be x
The cost of gumballs be y
and cost of chocolates be z
We are given that the gumballs cost 5 cents more than the chocolates
mathematically this can be written as
[tex]y=z+0.05[/tex]
Similarly,
The lollipops cost twice as much as the chocolates
mathematically this can be written as,
[tex]x=2z[/tex]
Now finally we purchase 3 gumballs, 2 lollipops and 7 chocolates
The equation can be given as,
[tex]3x+2y+7z=2.11[/tex]
Substituting the values of x and y in this equation we get,
[tex]6z+2(z+0.05)+7z=2.11\\6z+2z+0.1+7z=2.11\\15z=2.01\\z=0.134[/tex]
The cost of chocolates is $0.134
The cost of gumballs is $0.184
And the cost of lollipops is $0.268
Hence, The cost of lollipops, gumballs, chocolate is $ 0.268, $0.184, $0.134
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a rectangles width is 11 feet more than its length if the perimeter is 54 feet what is the length and width?
Let the length of the rectangle be l and the width be w
width is 11 feet more than length: we can write:
w = 11 + l
Also , perimeter is 54, we can write:
2l + 2w = 54
Note: Perimeter is sum of all sides
Now,
we replace 1st equation in 2nd and find l:
[tex]\begin{gathered} 2l+2w=54 \\ 2l+2(11+l)=54 \\ 2l+22+2l=54 \\ 4l=54-22 \\ 4l=32 \\ l=\frac{32}{4} \\ l=8 \end{gathered}[/tex]w is 11 + l
So,
width is 11 + 8 = 19
Length = 8 feet
Width = 19 feet
Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and v-intercept Slope - 9. y-intercepto 0.-)
the equation of the line will be
[tex]y+\frac{7}{9}=-9x[/tex]then subtracting 7/9 in both sides we have
[tex]y=-9x-\frac{7}{9}[/tex]which is the line equation in slope intercept form.
CALCULATOR COLOR THEME Q Q 4. Find the area of the shaded region. 4 in. 8 in. 4 in 12 in
We are asked to determine the area of the shaded region. there are two squares, to determine the area we need to find the area of the outer rectangle and subtract the area of the interior rectangle. Let's remember that the area of a rectangle is the product of its sides. Therefore, the area of the outer rectangle is:
[tex]\begin{gathered} A_0=(8in)(12in) \\ A_0=96in^2 \end{gathered}[/tex]Now we find the area of the interior rectangle:
[tex]\begin{gathered} A_i=(4in)(4in) \\ A_i=16in^2 \end{gathered}[/tex]Now we subtract the areas:
[tex]A=A_o-A_i[/tex]Replacing:
[tex]\begin{gathered} A=96in^2-16in^2 \\ A=80in^2 \end{gathered}[/tex]Therfore, the area of the shaded area is
/ Week 1 / Week 1 Monday - Daily Quiz
A rectangle is 5 feet long and 12 feet wide.
What is it's area?
60 feet² is the area of rectangle.
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.The four sides of a laptop are equal in length and have opposite sides that are parallel to one another.length = 5 feet
wide = 12 feet
area of rectangle = length × width
= 5 × 12
= 60 feet²
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