Each bag contains 20 pennies and we have 6 such bags.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information let the number of pennies in each bag is 'x'
and we have 6 such bags.
Therefore, The equation can be formed as,
6(10 + x) = 180.
60 + 6x = 180.
6x = 180 - 60.
6x = 120.
x = 120/6.
x = 20.
So, The number of pennies in each bag is 20.
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Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $1000 deposit in an account with an APR of 3%. The balance in the account after 1 year is approximately
The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
What is meant by continuous compounding?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.
Given,
rate per period = 3%
Principal amount = $1000
Compounding is done after 1,5 and 20 years.
But we are asked to find the amount after continuous compounding after 1 year.
The formula of the amount after continuous compounding is:
[tex]A = Pe^{rt}[/tex]
where A = amount after continuous compounding
r = rate of period
t = time period
P = principal amount
[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45
Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]
n = times it compounds per year = 365
r = 0.03
AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]
= 3.04%
Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
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2/12 Help me answer please
Answer:
Step-by-step explanation:
Let's call the present value of the loan P. The payments of $1,550 in 1 year and $2,400 in 4 years can be expressed as an ordinary annuity with semi-annual payments. We can calculate the present value of this annuity using the formula:
PV = A * (1 - (1 + r)^-n) / r
where
A = $1,550 / 2 = $775 (semi-annual payment)
n = (4 x 2) + 2 = 10 (number of semi-annual periods)
r = 0.045 / 2 = 0.0225 (semi-annual interest rate)
So,
PV = $775 * (1 - (1 + 0.0225)^-10) / 0.0225 = $8,100.40
Thus, the present value of the loan is P = $8,100.40.
Next, we can calculate the present value of the payment of $1,050 in 24 months and the balance in 30 months.
The payment of $1,050 in 24 months can be expressed as a single amount due in 24 months. The present value of this payment can be calculated as:
PV = $1,050 / (1 + 0.0225)^(24/2) = $1,000.54
So, the balance of the loan after this payment would be P - $1,000.54 = $8,099.86.
The balance in 30 months can be expressed as an ordinary annuity due with semi-annual payments. We can calculate the present value of this annuity using the formula:
PV = A * (1 - (1 + r)^-n) / r
where
A = ($8,099.86) / 6 = $1,349.98 (semi-annual payment)
n = 6 (number of semi-annual periods)
r = 0.0225 (semi-annual interest rate)
So,
PV = $1,349.98 * (1 - (1 + 0.0225)^-6) / 0.0225 = $7,999.86
Therefore, the payment required in 30 months for the rescheduled option to settle the loan is $1,349.98 per semi-annual period.
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Solve it but using the SQUARE ROOT PROPERTY
please help need ASAP!
The solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.
What is quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable in the equation is 2. The general form of a quadratic equation is:
ax^2 + bx + c = 0
where x is the variable, and a, b, and c are constants, with a not equal to 0. The quadratic equation can have two solutions, one solution, or no real solutions, depending on the values of a, b, and c.
Starting with the given equation:
25 = (x + 9)²
We can start by taking the square root of both sides of the equation, which gives us:
±5 = x + 9
Next, we can isolate x by subtracting 9 from both sides of the equation:
x = -9 ± 5
This gives us two solutions:
x = -9 + 5 = -4
or
x = -9 - 5 = -14
Therefore, the solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.
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A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $9 the average attendance has been 28000. When the price dropped to $7, the average attendance rose to 33000. Find a demand function D(q), where q is the quantity/number of the spectators. (Assume D(g) is linear) D(q) =
The demand function of the question is expressed as;
D(q) = -²/₅₀₀₀q + 14.6
How to find the Demand Function?The formula to find the slope between two coordinates is;
m = (y2 - y1)/(x2 - x1)
The coordinates we are given are;
(28000, 9) and (33000, 7)
Thus;
Slope; m = (7 - 9)/(33000 - 28000)
m = -2/5000
Now, the equation of a line in point slope form is;
y - y1 = m(x - x1)
Where (x1, y1) is (28000, 9)
y - 9 = (-2/5000)(x - 28000)
y - 9 = -²/₅₀₀₀x + 5.6
y = -²/₅₀₀₀x + 14.6
This can be rewritten as a demand function; D(q) = -²/₅₀₀₀q + 14.6
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Decide which of the two given prices is the better deal and explain why. You can buy shampoo in a 6-ounce bottle for $4.19 or in a 14-ounce bottle for $10.89.
Answer:
6-oz bottle is a better deal
Step-by-step explanation:
To find which is a better value, find the unit rates for both types of bottles
The bottle with the lower unit rate is the better deal
6-ounce bottle costs $4.19
Unit rate = 4.19/6 oz = $0.70 per oz
14-ounce bottle costs $10.89
Unit rate = 10.89/14 = $0.78 per oz
Hence the 6-oz bottle is a better deal
When put on a coordinate plane, 1st street has the equation y = 6x - 7. 2nd street is parallel to 1st street and
goes through the point (2, 9). Write the equation for 2nd Street in slope-intercept form.
by
The linear equation for the parallel line will be y=6x-3.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
Line parallel to line y=6x-7 will have same slope which will be m=6
as general equation is y=mx+c where m=slope and c=constant.
For parallel line c will be as it is passing through (2,9)
9=6*2+c
c=9-12
c=-3
then the equation will be y=6x-3
Hence,
The equation for the parallel line will be y=6x-3.
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please help i am so confused its eulerian circuit
According to the information in the graph, the cheapest route to travel through all cities would be: Atlanta - Dallas - San Francisco - Los Angeles - New York - Detroit - Atlanta.
How to calculate the cheapest option to travel to all cities?To calculate the cheapest option to travel to all cities, we must identify our starting point in the city of Atlanta and analyze which is the cheapest option to travel. In this case, it would be the Detroit or Dallas option (at this point we can choose either one).
Once we choose Dallas, we must apply a location strategy so that the next move leaves us in a suitable position to go to the cities of the east coast. Therefore, the best option would be San Francisco and then Los Angeles.
After this, the best (cheaper) option would be to take transportation to New York, Detroit, and finally to Atlanta. Finally, we must add the values of the displacements to know what the total value is:
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rewrite the equation in vertex form. y^2-4y-x+9=0
In the vertex form the equation can be rewritten as x = 1×(y - 2)² + 5
The equation is given in the standard form y²-4y-x+9 = 0 and we have to convert it into vertex form
So basically, the general vertex form of any equation is x = a(y - k)² + h
⇒ y²-4y-x+9 = 0
Shifting the x to RHS,
⇒ x = y²- 4y + 9
Writing y²- 4y in the form of (a-b)²,
⇒ x = y²- 4y + 4 + 5
⇒ x = 1×(y - 2)² + 5,
Hence the equation is now converted to vertex form
⇒ where a = 1, k = 2 and h = 5
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what is the slope of (-11,12) and (5,4)
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the following formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the points (-11, 12) and (5, 4), we get:
m = (4 - 12) / (5 - (-11)) = -8 / 16 = -1/2
So the slope of the line passing through (-11, 12) and (5, 4) is -1/2.
What is the value of k such that (x³ + x² - 9x - 36) + (x + 4) has a rernainder
of zero? Show your work.
Answer:x^3+x^2-8x-32
Step-by-step explanation:
Triangle XYZ is shown on the coordinate plane.
A triangle on the coordinate plane with vertices X at 0 comma 5, Y at 10 comma 3, and Z at 4 comma negative 1.
If triangle XYZ is translated using the rule (x, y) → (x + 2, y + 3) and then reflected across the x-axis to create triangle X″Y″Z″, what is the location of Z″?
(2, −8)
(6, −2)
(8, −2)
(12, −6)
The transformation of triangle XYZ vertices at X(0, 5), Y(10, 3), and Z(4, -1), indicates that the coordinate of the point Z'' following a composite transformation of a translation of (x, y) → (x + 2, y + 3), and a reflection across the x-axis, is located at the point (6, -2). The correct option is therefore;
(6, -2)What is a reflection transformation?A reflection transformation is a transformation that produces a mirror image of a geometric figure across a line of reflection.
The coordinates of the vertices of the triangle are;
X(0, 5), Y(10, 3), Z(4, -1)
The transformation rule that is used to translate the triangle ΔXYZ (to get ΔX'Y'Z'), can be presented as follows;
(x, y) → (x + 2, y + 3)The reflection of the translated figure of the triangle (ΔX'Y'Z'), to get ΔX''Y''Z'', is a reflection across the x-axis, therefore, we get;
The coordinates of the point (x, y) following a reflection across the x-axis is the point (x, -y)Therefore, we get the coordinate of the point (x, y) following the composite transformation is the point (x + 2, -(y + 3))
(x, -y) → (x + 2, -(y + 3))The coordinates of the point Y(4, -1) following the composite transformation is therefore;
Y(4, -1) → (4 + 2, -(-1 + 3)) = (6, -2)
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Talking on the telephone causes cancer.
6. There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answer:
(C) 29
Step-by-step explanation:
Answer:
the least possible number of marbles in the bag is 12.
Step-by-step explanation:
As for the question about the marbles, let's call the number of red marbles "x". Then the number of white marbles is 4x, the number of blue marbles is 5x, and the number of green marbles is (1/2) * 5x = 2.5x.
The total number of marbles in the bag is x + 4x + 5x + 2.5x = 12.5x.
To find the least possible number of marbles, we need to find the smallest possible value of x, which will give us the smallest total number of marbles. Since x represents the number of red marbles, it must be a positive integer. The smallest positive integer value of x is 1.
So, if there is one red marble, there are 4 white marbles, 5 blue marbles, and 2.5 green marbles. The total number of marbles in the bag is 1 + 4 + 5 + 2.5 = 12.5.
Therefore, the least possible number of marbles in the bag is 12.
What are the outliers in the data set? How do you know that they are outliers?
Step-by-step explanation:
you have to find your five number summary
You randomly survey middle school students and high school students about whether they prefer spring or winter. The results
are shown in the two-way table. Find the percent of middle school students that prefer each season and the percent of high school students that prefer each season.
Percentages are:
Middle school
Spring = 75% Winter = 25%
High school
Spring = 40% Winter = 60%
What is the percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Frequently, it is indicated with the per cent sign, "%". A percentage is a number without dimensions and without a standard measurement.
Given,
Middle school
Number of students preferring spring = 93
Number of students preferring winter = 31
High school
Number of students preferring spring = 36
Number of students preferring winter = 54
Total number of middle school students = 93 + 31 = 124
Percentage of middle school students who prefer spring = [tex]\frac{93}{124} * 100[/tex]
= 75%
Percentage of middle school students who prefer winter = [tex]\frac{31}{124} * 100[/tex] = 25%
Total number of high school students = 36+54 = 90
Percentage of high school students who prefer spring = [tex]\frac{36}{90} * 100[/tex]
= 40%
Percentage of high school students who prefer winter = [tex]\frac{54}{90} *100[/tex]
= 60%
Therefore the above is the percentage of students who prefer spring and winter.
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In AUVW, u = 6.7 inches, ZW=19° and ZU=5°. Find the area of AUVW, to the
nearest 10th of an square inch.
The required, area of the triangle to the nearest 10th of a square inch is 34.1 square inches.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°
Here,
Calculating unknown angle v,
Since the sum of the angles in the triangle is equal to 180,
u + w+ v = 180
5 + 19 + v = 180
v = 180 - 24
v = 156°
Now,
Calculating the unknown side w,
U/sinu = W/sinw
6.7/sin5° = W/sin19°
W =25.0277
Now,
Area of the triangle is given as
= 1/2 UW sinv
= 1/2× (25.027)×(6.7)×(sin156°)
= 34.1 square inch
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An observer standing at the top of a vertical cliff spots a house in the adjacent valley at an angle of depression of 12 degrees. The cliff is 60 meters tall. How far is the house from the base of the cliff?
Distance of the house from the base of the cliff is 282.27 m.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
From the figure attached,
AB = Height of the cliff = 60 m
Let the distance between the base of the cliff and the house 'C' = x m
If the angle of depression = 12°
Then angle of elevation of the top of the cliff from the house = 12°
Now from right triangle ABC,
tan12=60/x
x=60/tan 12
x=60/0.21256
x = 282.27 m
Therefore, distance of the house from the base of the cliff is 282.27 m.
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A faucet gives 20 gallons of water in 5 seconds. How many gallons does it give in 7 seconds?
Answer:
28
Step-by-step explanation:
IF 20 GALLONS IS EQUIVALENT TO 5 SECONDS WHAT ABOUT 7 SECONDS
CROSS MULTIPLY
Answer:
20 gallons / 5 seconds = 4 gallons / second
Therefore, In 7 seconds you get (7 x 4 ) or 28 gallons.
Step-by-step explanation:
3
10
x 100 = 0,3 x 100 =
Answer:
The answer is thirty (30)
Which equation represents a proportional relationship?
y=-x
y = 5x + 1
y = −5 (x + 1)
o y =15x
At the start of a party, a drink dispenser contains 912 quarts of iced tea. After the party only 7 cups of tea remain.How many cups of iced tea did people drink during the party?
Answer:
3,641 cups drank
Step-by-step explanation:
A quart is 4 cups
At the start of the party, there were 912 quarts, multiply that by 4 to get 3,648 cups
At the end of the party, only 7 cups remained
3648 - 7 = 3,641 cups drank
An angle measures 17.4° more than the measure of its complementary angle. What is the measure of each angle?
45 and 27.6 degrees are the two complementary angles.
What are the angles' measurements?The various angles or measurements include:
Measure an acute angle between 0° and 90°.Measure the obtuse angle between 90° and 180°.Right Angle: The measurement is 90 degrees.Straight Angle: The measurement is 180 degrees.Measure the reflex angle from 180° to 360°.Complete or full angle: 360° is the exact measurement.Angles that are complementary are those whose sum is 90 degrees. If the smaller angle has a measure of x, then the complementary angle's measure is 90 - x.
The issue shows that the greater angle (x + 17.4) is 17.4 degrees larger than the corresponding angle's measurement (90 - x). To find x, we can construct the following equation:
x + 17.4 = 90 - x + 17.4
When we simplify and find x, we obtain:
2x = 55.2
x = 27.6
The greater angle's measure is x + 17.4 = 45 degrees, while the smaller angle's measure is x = 27.6 degrees.
The two complementary angles are 27.6 and 45 degrees as a result.
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*Image*
Find the value of x.
The value of the exterior angle x of the quadrilateral is equal to
How to evaluate for the exterior angle xThe sum of the exterior angles of any convex quadrilateral is 360 degrees so we have that:
65 + 106 + 78 + x = 360
simply the left hand side of the equation
249 + x = 360
subtract 249 from both sides of the equation
249 - 249 + x = 360 - 249
x = 111°
In conclusion, since the sum of the exterior angles of a quadrilateral is s 360°, we have got the measure of one the the exterior angle x to be equal to 111°
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If Gabe buys 20 yards of fabric, uses 6 2/3 yards to make some pillow cases and another 10 1/4 yards to make curtains for his room, how many yards of fabric will he have left?
Answer:
3 and 1/12 left
Step-by-step explanation:
Please I could really use some help
Answer:
-1/2
Step-by-step explanation:
cos(-360+60)=-1/2
[tex]\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ -300\implies 30-330\hspace{5em}\cos(-300^o)\implies \cos(30^o-330^o) \\\\\\ \cos(30^o-330^o)\implies \cos(30^o)\cos(330^o)+\sin(30^o)\sin(330^o) \\\\\\ \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{3}}{2}~~ + ~~\cfrac{1}{2}\cdot \cfrac{-1}{2}\implies \cfrac{3}{4}~~ + ~~\cfrac{-1}{4}\implies \cfrac{3}{4}-\cfrac{1}{4}\implies \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}[/tex]
Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the Green were Planes?
There are 16% of the Green were Planes.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Total number of green planes = 250
The total number of all planes = 1550
The percent of green planes = (number of green planes/number of total planes ) x 100
The percent of green planes = (250/1550) x 100
The percent of green planes = 0.1612 x 100
The percent of green planes = 16.129
Round to the nearest percent, and we get
The percent of green planes = 16%
Thus, 16% of the Green were Planes.
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Sami is 5 feet 8 inches tall and his younger sister is 4 feet 11 inches tall. How many inches taller is sami than his sister?.
The number of inches Sami is taller to his younger sister as per their respective given heights is equal to 9 inches.
Height of Sami in feet and inches is equal to 5 feet 8 inches
Height of Sami's younger sister is equal to 4 feet 11 inches
Convert all height into inches we get,
1 feet = 12inches
5 feet = 5 × 12 inches
= 60 inches
4 feet = 4 × 12 inches
= 48 inches
Number of inches Sami's is taller than his younger sister is equal to
= ( 5 feet 8 inches ) - ( 4 feet 11 inches )
= ( 60 + 8 ) inches - ( 48 + 11 ) inches
= 68 inches - 59 inches
= 9 inches
Therefore, the number of inches Sami is taller than his younger sister is equal to 9 inches.
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find the value of each variable provide proofs
x= 19, y=19
There is a theorem with 45 degrees 45 degrees 90 degrees triangles, it is that the two legs are equal to a and the hypotenuse is equal to a√2
So, since we know the hypotenuse is 19√2, a=19
so x = 19and y = 19
What is (−2) ( 3 4/7 ) ? step by step
Answer:-50/7 or -7.143
Step-by-step explanation:
you have to turn the 3 4/7 into an improper fraction by this:
3x7=21
21+4=25
which makes it 25/7
(25/7)x(-2) = -50/7 or -7.143
using addition and subtraction signs make 1 2 3 4 5 6 7 8 9 equal 30
The numbers can be arranged as follows
(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30 How to solve the math questionThe math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
Applying the sequence the to make the expression 1 2 3 4 5 6 7 8 9 equal to 30 using addition and subtraction signs:
(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30
You can use parentheses to group the numbers and then add or subtract the groups to get the desired result.
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Help me with this Quadratic function graph the function
The graph of the quadratic function can be seen on the image at the end.
How to graph the quadratic function?The only way to graph or sketch a function by hand, is by finding some points on the graph and then connecting them.
To find the points we need to evaluate the quadratic equation.
if x = 0
y = 5*0^2 + 2 = 2
So we have the point (0, 2)
if x = 1
y = 5*1^2 + 2 = 7
So we have the point (1, 7)
if x = -1
y = 5*(-1)^2 + 2 = 7
So we have the point (-1, 7)
And so on, once you have enough points, you can graph them on the coordinate axis and then connect them. The graph of the quadratic equation can be seen on the image at the end.
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