Cara has saved 1, 430 pennies. She needs to put the pennies in paper rolls so the bank can count them easily. Each penny roll holds 50 pennies. The number of pennies will be in the last roll is 30.
To find out the number of pennies will be in the last roll.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given that:
Cara has saved 1, 430 pennies.
Each penny roll holds 50 pennies.
1430 divides by 50 = 143/5≈29 roles and in last roll it will be 30 pennies.
So, the number of pennies will be in the last roll is 30.
Learn more about arithmetic here:
https://brainly.com/question/28092210
#SPJ1
1!+2(2!)+3(3!)+...+n(n!)=(n+1)!-1
Step-by-step explanation:
OK, let's assume it this way:
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+...+(n+1)!-n!=(n+1)!-1!=(n+1)!-1
and boom problem solved
Using the data in the table, which statement is true?
The true statement is mean > median
How to determine the true statement?The mean is the average value.
So, we have
Mean = Sum/Count
This gives
Mean = (8 * 1 + 10 * 3 + 14 * 2)/(1 + 3 + 2)
Evaluate
Mean = 11
The mode is the measure with the highest frequency.
So, we have
Mode = 10
The median is the middle element
So, we have
Median = 10
The mean (11) is greater than the mode and the median
Hence, the true statement is mean > median
Read more about mean, median and mode at:
https://brainly.com/question/15323584
#SPJ1
From atop a 15 m lighthouse, a man spots a dolphin 50 m out to sea. Find the angle of depression from the man to the dolphin, to nearest degree.
Answer:
16.7 degrees
Step-by-step explanation:
how to be smart
please help
A restaurant hands out a scratch-off game ticket with prizes being worth
purchases at the restaurant. The back of the ticket lists the odds of winning
each dollar value: 0.4 for $10, 0.2 for $25, 0.01 for $30, and 0.004 for $75.
What are the odds that the ticket is worth at least $25?
Using the probability concept, the odds that the ticket is worth at least $25 are of 1:3.67.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering the probability, the odd is given by:
o = probability:(1 - probability)
From the given table, the probability that the ticket is worth at least $25 is:
p = 0.2 + 0.01 + 0.004 = 0.214.
Hence the odd is:
o = 0.214/(1 - 0.214) = 0.214/0.786 = 1:3.67.
More can be learned about odds and probability at https://brainly.com/question/16363997
#SPJ1
Place value in thousands for the 0 in 10000
The place value in thousands for the 0 in 10000 is 0 thousands
Place valueFrom the question, we are to the determine the place value in thousands for the 0 in the given number
The given number is
10000
The place value in thousands for the 0 in 10000 is 0 thousands
Hence, the place value in thousands for the 0 in 10000 is 0 thousands
Learn more on Place value here: https://brainly.com/question/627658
#SPJ1
NO LINKS!! Please help me with this problem.
What is the standard form of the equation of the ellipse?
Answer:
[tex]\dfrac{x^2}{49}+\dfrac{y^2}{36}=1[/tex]
Step-by-step explanation:
From inspection of the given graph, we can see that the center of the ellipse is the origin (0, 0) and the longest diameter of the ellipse is across the x-axis.
Therefore, we can use the general equation of a horizontal ellipse with its center at (0, 0):
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where:
center = (0, 0)Vertices = (±a, 0)Co-vertices = (0, ±b)Foci = (±c, 0) where c²=a²−b²Major Axis: longest diameter (2a)Minor Axis: shortest diameter (2b)Major radius: one half of the major axis (a)Minor radius: one half of the minor axis (b)From inspection of the ellipse:
Vertices = (-7, 0) and (7, 0)Co-vertices = (0, 6) and (0, -6)Therefore, a = 7 and b = 6
Substitute the found values of a and b into the formula:
[tex]\implies \dfrac{x^2}{7^2}+\dfrac{y^2}{6^2}=1[/tex]
[tex]\implies \dfrac{x^2}{49}+\dfrac{y^2}{36}=1[/tex]
Learn more about ellipses here:
https://brainly.com/question/28152346
https://brainly.com/question/28144085
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given figure shows a Horizontal Ellipse with its centre at origin, and as we observe the figure, we can conclude that :
Length of major axis is :
[tex]\qquad \sf \dashrightarrow \: 2a = 14[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 7[/tex]
and that of minor axis :
[tex]\qquad \sf \dashrightarrow \: 2b = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: b = 6[/tex]
Equation of Ellipse will be ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {a}^{2} } + \dfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
[ plug in the values ]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {7}^{2} } + \dfrac{ {y}^{2} }{ {6}^{2} } = 1[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {49}^{} } + \dfrac{ {y}^{2} }{ {36}^{} } = 1[/tex]
how many lines of symmetry does this figure have
Answer:
14 and please Mark me brainlist
Answer:
There are four lines of symmetry in this figure.
Step-by-step explanation:
First look at the mainframe, it has 2 lines of symmetry. And if you look at it diagonally, it has another 2 more lines.
So therefore there is 4 lines of symmetry in this H figure.
Please mark me the Brainliest!
a. If you wanted to draw a circle around this triangle that passed through points A, B, and C as shown by circle P, what steps would you take to do that? b. What steps would you take to draw a circle within the triangle such that each side of the triangle became a tangent line to the circle as shown by circle R? c. If a line drawn from point B to point P measures 2 inches, what is the diameter, circumference, and area of circle P in terms of I? d. Describe how you would find the area of the region bounded by segment BC and arc BDC in terms of a if the arc measure of arc BDC is 60°
The circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.
Steps involved in inscribing a triangleThe steps involved in inscribing a triangle;
Construct two chords on the circle.Then , draw a perpendicular bisector to the chords with the compass which must meet at the center of the circle. Make a line from the center to one of the farthest points of the chords.Draw two lines to form a 30 degree with the radius on the opposite side.Stretch out these two lines to make two chords on the circle. The two chords should make angle of 60 degrees to each other.Then connect the other extreme of the two chords this makes an equilateral triangle.If the line drawn from point B to point P measures 2 inches, then the diameter is
= 2 × 2
= 4 inches.
The formula for calculating the circumference of a circle is given as;
Circumference = 2 π r
Radius = diameter/ 2
Radius = 4/2 = 2 Inches
Substitute the values
Circumference = 2 × 3. 142 × 2
Circumference = 12. 57 inches
Area = π r²
Area = 3. 142 × 2²
Area = 3. 142 × 4
Area = 12. 57 square inches
Thus, the circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.
Learn more about a circle here:
https://brainly.com/question/15673093
#SPJ1
Evaluate 8xy+16y/5x
if x = 4 and y=-5.
A-42
B-7
C-23
D-12
Answer:
D
Step-by-step explanation:
substitute x = 4 , y = - 5 into the expression
[tex]\frac{8(4)(-5)+16(-5)}{5(4)}[/tex]
= [tex]\frac{-160-80}{20}[/tex]
= [tex]\frac{-240}{20}[/tex]
= - 12
What is the frequency of the function f (x). f (x) = -2sin x/4 +3
Answer: [tex]8\pi[/tex]
Step-by-step explanation:
The period is [tex]\frac{2\pi}{1/4}=8\pi[/tex].
I
23
12
N
L
12
23
O
K
M
18
18
Answer: [tex]\sqrt{407}[/tex]
Step-by-step explanation:
In this triangle, we know that [tex]IJ=46, IK=24, JK=36[/tex].
So, using the Law of Cosines in triangle IJK,
[tex]36^2 = 46^2 + 24^2 - 2(46)(24) \cos (\angle JIK)\\\\-1396=-2(46)(24) \cos(\angle JIK)\\\\\cos (\angle JIK)=\frac{349}{552}[/tex]
Using the Law of Cosines in the triangle LIK,
[tex](KL)^2 = 23^2 + 24^2 - 2(23)(24) \cos (\angle JIK)\\\\(KL)^2 = 23^2 + 24^2 - 2(23)(24)\left(\frac{349}{552} \right)\\\\(KL)^2 = 407\\\\KL=\sqrt{407}[/tex]
The function f and g are given by [tex]f(x)=x^2[/tex] and [tex]g(x)=-^1_2 x+5[/tex].
Let R be the region bounded by the x-axis and the graphs f and g as shown at the bottom. Also, I only need you to answer part b, I've already finished part a.
a) Describe how you would find the area of R.
[tex]R=18 \frac{2}{3}[/tex]
b) The region R is the base of a solid. For each y, where
0 < y < 4, the cross-section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 3y. Explain how you would write an expression that gives the volume of the solid.
As you've pointed out, R is a different region that I originally thought. The area of R can be computed using either
[tex]\displaystyle \int_0^2 x^2 \, dx + \int_2^{10} -\frac x2 + 5 \, dx[/tex]
or
[tex]\displaystyle \int_0^4 (10-2y)-\sqrt y \, dy[/tex]
Either way, you've gotten the correct area for part (a).
For part (b), we can use part of the integral with respect to [tex]y[/tex] above. The horizontal distance between the curves [tex]y=x^2[/tex] and [tex]y=-\frac x2+5[/tex] is obtained by first solving for [tex]x[/tex],
[tex]y=x^2 \implies x=\sqrt y[/tex]
[tex]y=-\dfrac x2+5 \implies x = 10-2y[/tex]
so the length of each cross section is [tex]10-2y-\sqrt y[/tex].
The height of each cross section is [tex]3y[/tex].
Then the volume of the solid is
[tex]\displaystyle \int_0^4 3y \left(10-2y-\sqrt y\right) \, dy = \boxed{\int_0^4 -6y^2 + 30y - 3y^{3/2} \, dy}[/tex]
The instructions don't say to evaluate, but if you're looking for practice the volume ends up being 368/5, or 73 3/5.
What is the value of x when (f o g)(x) =-8
Answer:
I think the answer is 3.
Step-by-step explanation:
First make arrow diagram of function f and g.
Then show it as composite function of fog(x) in arrow diagram.
Then in range you find -8 whose domain as x is 3.
What is the equation of the directrix?
The equation of the directrix is y = -5
How to determine the directrix equation?The equation is given as:
(x -1)^2 = 12(y + 2)
Express 12 as a product of 4 and 3
(x -1)^2 = 4 * 3(y + 2)
The parabola is represented as:
(x -h)^2 = 4p(y - k)
Where the directrix is
y = k - p
By comparison, we have:
k = -2 and p = 3
So, we have:
y = -2 - 3
Evaluate
y = -5
Hence, the equation of the directrix is y = -5
Read more about directrix at:
https://brainly.com/question/2131669
#SPJ1
You deposit $4000 each year into an account earning 2% interest compounded annually. How much will you have in the account in 30 years?
The amount that will be in the account after 30 years is $162,272.32.
How much would be in the account after 30 years?When an amount is compounded annually, it means that once a year, the amount deposited and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.
The formula that can be used to determine the future value of the yearly deposit of $4,000 in 30 years is : annuity factor x yearly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest raten = number of years$4000 x [{(1.02^30) - 1} / 0.02] = $162,272.32
To learn more about calculating the future value of an annuity, please check: brainly.com/question/24108530
#SPJ1
log a^x² - 9log a³√x simplify
Answer:
log(a^x^2-27(radicalx))
Step-by-step explanation:
Assuming you have written your question correctly, this is it.
Find the interest rate for a principal of $6514 and charged $45415 in interest for 15 years.
Answer:
the answer is 46.47937775048613
Example 2.11: Solve the following
a) 4x² +10x = 6
Answer:
[tex]\huge\boxed{\sf \{-3, 1/2\}}[/tex]
Step-by-step explanation:
Given equation:4x² + 10x = 6
Take 2 common
2(2x² + 5x) = 6
Divide 2 to both sides
2x² + 5x = 3
Subtract 3 to both sides
2x² + 5x - 3 = 0
Using mid-term break
2x² + 6x - x - 3 = 0
Take common
2x(x + 3) - 1(x + 3) = 0
Take (x + 3) common
(x + 3)(2x - 1) = 0
Either,
x + 3 = 0 OR 2x - 1 = 0
x = -3 OR 2x = 1
x = -3 OR x = 1/2
Solution Set = {-3, 1/2}[tex]\rule[225]{225}{2}[/tex]
Answer: x = 3 or (-1/2)
Step-by-step explanation:
Given equation
4x² + 10x = 6
Subtract 6 on both sides
4x² + 10x - 6 = 6 - 6
4x² + 10x - 6 = 0
Use cross-multiplication to factorize the quadratic
Starting with:
2x -6
2x 1
This gives us:
(2x - 6) (2x + 1) = 0
Assume each value in the parenthesis to be 0
PART I:
2x - 6 = 0 ⇒ Given equation
2x - 6 + 6 = 0 + 6 ⇒ Add 6 on both sides
2x / 2 = 6 / 2 ⇒ Divide 2 on both sides
[tex]\boxed{x=3}[/tex]
PART II:
2x + 1 = 0 ⇒ Given equation
2x + 1 - 1 = 0 - 1 ⇒ Subtract 1 on both sides
2x / 2 = -1 / 2 ⇒ Divide 2 on both sides
[tex]\boxed{x=-\frac{1}{2} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
How to solve for X in the triangle
Answer:
22.6
Step-by-step explanation:
a^2+b^2=c^2
8^2+b^2=24^2
b^2=512
b=22.6
Answer:
[tex]x = 16\sqrt{2}[/tex]
Step-by-step explanation:
we are given a right triangle.
then
In order to determine x we need to use
the Pythagorean theorem:
[tex]x^{2}+8^{2}=24^{2}[/tex]
⇔ x² + 64 = 576
⇔ x² = 576 - 64
⇔ x² = 512
⇔ x² = 2⁹
⇔ x² = 2 × 2⁸
[tex]\Longleftrightarrow x=\sqrt{2\times 2^{8}} =\sqrt{2\times \left( 2^{4}\right)^{2} }[/tex]
[tex]\Longleftrightarrow x= \sqrt{\left( 16\right)^{2} } \times \sqrt{2[/tex]
[tex]\Longleftrightarrow x = 16\sqrt{2}[/tex]
0.1in has 4 threads how many threads are in 1 inch?
Answer:
40
Step-by-step explanation:
Set up a proportion
Inch/ threads = inch to threads
.1/4 = 1/x Cross multiple
.1x = 4 Divide both sides by .1
x = 40
2. Which of the following graphs show a function with domain 1 ≤ x ≤ 6? Select two that
apply.
Answer:
Graphs A and B
Step-by-step explanation:
Graphs A & B are using x-values 1-6 and stop there, which is what the domain is trying to find. Though, for the other graphs, these graphs are rather starting at 1 via the domain, while not going up to 6 on the domain.
a display at an aquarium has sea stars to wolf eels in a ratio 4 : 5. It also has 5/8 as many rockfish as sea stars. there are 40 more wolf eels than rock fish. How many sea stars are there?
The number of sea stars is 64.
What is a ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.
In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."
This ratio is expressed in fraction form as a/b. We utilize the same method for further simplifying a ratio as we use for further simplifying a fraction.
According to the question,
Ratio of sea stars to wolf eels = 4:5
Number of rock fish= 5/8 (Number of sea stars)
Number of wolf eels - Number of rock fish = 40
Using the given information, we get,
Number of sea stars = 8/5 (Number of rock fish)
On simplification,
Number of wolf eels = 80
So, number of sea stars = (4/5)*80
= 64
Learn more about ratios here:
https://brainly.com/question/2328454
#SPJ1
The perimeter of a right angled triangle, with hypotenuse c=101cm and one side b=20cm, is:
Answer:
220
Step-by-step explanation:
We need to find the 3rd side length
We already know the hypotenuse and one side, so we can use the Pythagorean formula.
101^2 = a^2 + 20^2. A is the third side, and solving for it, we find that it equals 99.
Side 1 = 101
Side 2 = 99
Side 3 = 20
101 + 99 + 20 = 220
What will it cost to carpet a rectangular floor measuring 21 feet by 18 feet if the carpet costs $25.68 per square yard?
$1078.56
What is the formula of the area of the rectangle?The formula of the area of the rectangle = Length * Breadth
= 18*21 feet
= 378 feet^2
As cost of carpet is given in square yard. so convert area of rectangle in square yard.
1 square feet = 9 square yard
so, 378/9 = 42 square yard
Cost of carpet = $ 25.68 per square yard (given)
Total cost of rectangular floor = 25.68 * 42
= $1078.56 square yard
To learn more please refer: https://brainly.com/question/2607596
#SPJ9
$1078.56 is the cost to carpet a rectangular floor measuring 21 feet by 18 feet if the carpet costs $25.68 per square yard.
What will it cost to carpet a rectangular floor?Given:
A rectangular floor measuring 21 feet by 18 feet.The carpets cost $25.68 per square yard.Find:
Cost to carpet a rectangular floor.Solution:
The formula of the area of the rectangle = Length * Breadth
= 18*21 feet
= 378 feet^2
As the cost of the carpet is given in square yard. so convert an area of the rectangle into a square yard.
1 square foot = 9 square yards
so, 378/9 = 42 square yard
Cost of carpet = $ 25.68 per square yard (given)
Total cost of rectangular floor = 25.68 * 42
= $1078.56 square yard
To learn more about rectangular, refer to:
brainly.com/question/2607596
#SPJ9
Point One = (0, -2)
Point Two = (-3,-5)
Slope-Intercept Form
Answer:
y = x - 2
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this formula, "m" represents the slope and "b" represents the y-intercept. Before writing our equation in this form, we first need to find the slope. The slope can be found using the point-slope formula:
y₁ - y₂ = m(x₁ - x₂)
In this formula, "m" represents the slope, "x₁" and "y₁" represent the values from Point One, and "x₂" and "y₂" represent the values from Point Two. You can find the slope by plugging the values from the points into the equation and then simplifying.
x₁ = 0 x₂ = -3
y₁ = -2 y₂ = -5
y₁ - y₂ = m(x₁ - x₂)
(-5 - (-2)) = m(-3 - 0)
-3 = m(-3)
1 = m
Now that we have a value for the slope, we can use the values from either one of the points to solve for the y-intercept (from the slope-intercept form equation).
m = 1
x = 0
y = -2
y = mx + b
-2 = (1)(0) + b
-2 = 0 + b
-2 = b
Therefore, the equation of the line in slope-intercept form is:
y = x - 2
4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the diameter of the circle x² + y² - 4x - 4y +4= 0
The standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .
How to find the standard equation of a hyperbolaIn this problem we must determine the equation of the hyperbola in its standard form from the coordinates of the foci and a general equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:
(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)
(h, k) = (2, 2)
To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the general equation of the circle into its standard form.
If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:
x² + y² - 4 · x - 4 · y + 4= 0
(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4
(x - 2)² + (y - 2)² = 2²
The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:
V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)
And the distance from the center to any of the vertices is 2 (semi-major distance, a) and the semi-minor distance is:
b = √(c² - a²)
b = √(3² - 2²)
b = √5
Therefore, the standard form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .
To learn more on hyperbolae: https://brainly.com/question/27799190
#SPJ1
An administer of a college believes that 40% students of the college work in part time. He
randomly surveyed of 2,512 students and finds that 1,298 of them work in part time, that is, about 51.7% of
the student being surveyed work in part time.
1.
Is the study observational or experimental?
2.
What is the population of interest?
3.
What is the parameter of interest?
4.
What is the sample in the study?
5.
What is the statistic involved?
See below for the response to each question
Is the study observational or experimental?The study is experimental.
This is so because, the administer surveyed random college students
The population of interestThis is the total number of students in the college
Hence, the population of interest is the students in the college
The parameter of interestThis is the value that gives the required information.
Hence, the parameter of interest is the proportion of college students that work part-time
The sample in the studyThis is the students that were randomly surveyed
Hence, the sample in the study is the 2,512 students that were randomly surveyed
What is the statistic involvedThe statistic is the sample mean
Read more about random surveys at:
https://brainly.com/question/15105321
#SPJ1
Write the positive or negative number that best
represents the given information.
12 ft above sea level
Answer:
12
Step-by-step explanation:
Usually, above sea level is represented by a positive number and below sea level by a negative number.
12 ft above sea level = 12
Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''. Which of the following statements is true for ΔABC and ΔA''B''C''?
Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''.
Hence:
Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1